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Глава 7. Дерево
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Глава 7. Дерево
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7.1 Двоичное дерево
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Глава 8. Куча
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8.1 Куча
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Глава 9. Граф
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Глава 9. Граф
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9.1 Граф
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9.2 Базовые операции над графами
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9.3 Обход графа
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9.4 Резюме
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Глава 10. Поиск
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10.1 Двоичный поиск
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10.2 Точка вставки двоичного поиска
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10.3 Граничные случаи двоичного поиска
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10.4 Стратегия оптимизации через хеширование
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10.5 Алгоритмы поиска: новый взгляд
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10.6 Резюме
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Глава 11. Сортировка
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Глава 11. Сортировка
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11.1 Алгоритмы сортировки
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11.2 Сортировка выбором
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11.3 Пузырьковая сортировка
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11.4 Сортировка вставкой
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11.5 Быстрая сортировка
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11.6 Сортировка слиянием
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11.7 Пирамидальная сортировка
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11.8 Блочная сортировка
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11.9 Сортировка подсчетом
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11.10 Поразрядная сортировка
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11.11 Резюме
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Глава 12. Разделяй и властвуй
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12.1 Алгоритмы разделяй и властвуй
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12.2 Стратегия поиска разделяй и властвуй
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12.3 Задача построения двоичного дерева
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12.4 Задача о Ханойской башне
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12.5 Резюме
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Глава 13. Поиск с возвратом
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13.1 Алгоритм поиска с возвратом
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13.2 Задача о перестановках
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13.3 Задача о сумме подмножеств
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<h1 id="23">2.3 &nbsp; Временная сложность<a class="headerlink" href="#23" title="Permanent link">&para;</a></h1>
<p>Время выполнения может наглядно и точно отражать эффективность алгоритма. Если мы хотим точно оценить время работы некоторого фрагмента кода, как это сделать?</p>
<ol>
<li><strong>Определить платформу выполнения</strong>, включая конфигурацию оборудования, язык программирования, системную среду и т.д., поскольку все эти факторы влияют на эффективность выполнения кода.</li>
<li><strong>Оценить время выполнения различных вычислительных операций</strong>, например операция сложения <code>+</code> требует 1 нс , операция умножения <code>*</code> требует 10 нс , операция вывода <code>print()</code> требует 5 нс и т.д.</li>
<li><strong>Подсчитать все вычислительные операции в коде</strong> и суммировать время выполнения всех операций, чтобы получить общее время работы.</li>
</ol>
<p>Например, в следующем коде размер входных данных равен <span class="arithmatex">\(n\)</span> :</p>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># На некоторой платформе выполнения</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1"># 1 нс</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1"># 1 нс</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1"># 10 нс</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># Цикл выполняется n раз</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="c1"># 1 нс</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># 5 нс</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// На некоторой платформе выполнения</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 10 нс</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 нс</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5 нс</span>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># На некоторой платформе выполнения</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># 1 нс</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 1 нс</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># 10 нс</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="c1"># Цикл выполняется n раз</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="c1"># 1 нс</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 5 нс</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<p>Согласно приведенному выше методу, время работы алгоритма равно <span class="arithmatex">\((6n + 12)\)</span> нс :</p>
<div class="arithmatex">\[
1 + 1 + 10 + (1 + 5) \times n = 6n + 12
\]</div>
<p>Но на практике <strong>подсчитывать реальное время выполнения алгоритма и неразумно, и нереалистично</strong>. Во-первых, мы не хотим привязывать оценку времени к конкретной платформе, потому что алгоритм должен запускаться на самых разных платформах. Во-вторых, нам трудно узнать время выполнения каждого типа операций, а это сильно усложняет оценку.</p>
<h2 id="231">2.3.1 &nbsp; Подсчет тенденции роста времени<a class="headerlink" href="#231" title="Permanent link">&para;</a></h2>
<p>Анализ временной сложности оценивает не само время выполнения алгоритма, <strong>а тенденцию роста этого времени по мере увеличения объема данных</strong>.</p>
<p>Понятие "тенденции роста времени" довольно абстрактно, поэтому разберем его на примере. Предположим, размер входных данных равен <span class="arithmatex">\(n\)</span> , и даны три алгоритма <code>A</code> , <code>B</code> и <code>C</code> :</p>
<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="c1"># Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000000</span><span class="p">):</span>
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="p">}</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="p">}</span>
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="p">}</span>
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="p">}</span>
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmA</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmB</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="p">}</span>
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a>
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmC</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1_000_000</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="p">}</span>
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="p">}</span>
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">}</span>
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="mi">1000000</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="p">}</span>
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1">// Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algoritm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="p">}</span>
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="c1">// Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">){</span>
<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="p">}</span>
<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="c1">// Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="m">1000000</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1"># Временная сложность алгоритма A: постоянная</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="k">end</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="c1"># Временная сложность алгоритма B: линейная</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="k">end</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="c1"># Временная сложность алгоритма C: постоянная</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="mi">1_000_000</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<p>На рисунке 2-7 показана временная сложность трех функций алгоритмов выше.</p>
<ul>
<li>У алгоритма <code>A</code> есть только 1 операция вывода, и время его работы не растет с увеличением <span class="arithmatex">\(n\)</span> . Мы называем такую временную сложность "постоянной".</li>
<li>В алгоритме <code>B</code> операция вывода выполняется в цикле <span class="arithmatex">\(n\)</span> раз, поэтому время работы растет линейно по мере увеличения <span class="arithmatex">\(n\)</span> . Такая временная сложность называется "линейной".</li>
<li>В алгоритме <code>C</code> операция вывода выполняется <span class="arithmatex">\(1000000\)</span> раз; хотя время работы велико, оно не зависит от размера входных данных <span class="arithmatex">\(n\)</span> . Поэтому временная сложность <code>C</code> такая же, как у <code>A</code> , и тоже является "постоянной".</li>
</ul>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_simple_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Тенденции роста времени для алгоритмов A, B и C" class="animation-figure" src="../time_complexity.assets/time_complexity_simple_example.png" /></a></p>
<p align="center"> Рисунок 2-7 &nbsp; Тенденции роста времени для алгоритмов A, B и C </p>
<p>Какие особенности имеет анализ временной сложности по сравнению с непосредственным измерением времени работы алгоритма?</p>
<ul>
<li><strong>Временная сложность позволяет эффективно оценивать эффективность алгоритма</strong>. Например, время работы алгоритма <code>B</code> растет линейно: при <span class="arithmatex">\(n &gt; 1\)</span> он медленнее алгоритма <code>A</code> , а при <span class="arithmatex">\(n &gt; 1000000\)</span> медленнее алгоритма <code>C</code> . На самом деле, если размер входных данных <span class="arithmatex">\(n\)</span> достаточно велик, алгоритм с "постоянной" сложностью обязательно лучше алгоритма с "линейной" сложностью. В этом и состоит смысл тенденции роста времени.</li>
<li><strong>Метод вывода временной сложности проще</strong>. Очевидно, что платформа выполнения и тип вычислительных операций не влияют на тенденцию роста времени работы алгоритма. Поэтому в анализе временной сложности мы можем считать время выполнения всех вычислительных операций одинаковым "единичным временем" и тем самым упростить "подсчет времени выполнения операций" до "подсчета количества операций", что существенно снижает сложность оценки.</li>
<li><strong>У временной сложности есть и определенные ограничения</strong>. Например, хотя временная сложность алгоритмов <code>A</code> и <code>C</code> одинакова, их реальное время выполнения сильно различается. Точно так же, хотя временная сложность <code>B</code> выше, чем у <code>C</code> , при малых <span class="arithmatex">\(n\)</span> алгоритм <code>B</code> явно лучше <code>C</code> . В таких случаях нам часто трудно судить об эффективности алгоритма, опираясь только на временную сложность. Тем не менее, несмотря на эти ограничения, анализ сложности все равно остается самым эффективным и самым распространенным способом оценки алгоритмов.</li>
</ul>
<h2 id="232">2.3.2 &nbsp; Асимптотическая верхняя граница функции<a class="headerlink" href="#232" title="Permanent link">&para;</a></h2>
<p>Для функции с входным размером <span class="arithmatex">\(n\)</span> :</p>
<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># +1</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1"># +1</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1"># +1</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a> <span class="c1"># Цикл выполняется n раз</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="c1"># +1</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># +1</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="p">{</span>
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a>
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="c1">// Цикл выполняется n раз</span>
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (каждый раз выполняется i ++)</span>
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># +1</span>
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># +1</span>
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># +1</span>
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w"> </span><span class="c1"># Цикл выполняется n раз</span>
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="c1"># +1</span>
<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># +1</span>
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<p>Пусть количество операций алгоритма является функцией от размера входных данных <span class="arithmatex">\(n\)</span> и обозначается как <span class="arithmatex">\(T(n)\)</span> ; тогда для приведенной выше функции число операций равно:</p>
<div class="arithmatex">\[
T(n) = 3 + 2n
\]</div>
<p><span class="arithmatex">\(T(n)\)</span> - линейная функция, а это означает, что тенденция роста времени работы линейна, следовательно, ее временная сложность является линейной.</p>
<p>Линейную временную сложность мы записываем как <span class="arithmatex">\(O(n)\)</span> ; этот математический символ называется <u>нотацией Big <span class="arithmatex">\(O\)</span> (big-<span class="arithmatex">\(O\)</span> notation)</u> и обозначает <u>асимптотическую верхнюю границу (asymptotic upper bound)</u> функции <span class="arithmatex">\(T(n)\)</span> .</p>
<p>По сути анализ временной сложности - это вычисление асимптотической верхней границы "количества операций <span class="arithmatex">\(T(n)\)</span>", и у него есть строгое математическое определение.</p>
<div class="admonition note">
<p class="admonition-title">Асимптотическая верхняя граница функции</p>
<p>Если существуют положительное действительное число <span class="arithmatex">\(c\)</span> и действительное число <span class="arithmatex">\(n_0\)</span> , такие что для всех <span class="arithmatex">\(n &gt; n_0\)</span> выполняется <span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span> , то можно считать, что <span class="arithmatex">\(f(n)\)</span> задает асимптотическую верхнюю границу для <span class="arithmatex">\(T(n)\)</span> ; это записывается как <span class="arithmatex">\(T(n) = O(f(n))\)</span> .</p>
</div>
<p>Как показано на рисунке 2-8, вычислить асимптотическую верхнюю границу - значит найти такую функцию <span class="arithmatex">\(f(n)\)</span> , что при стремлении <span class="arithmatex">\(n\)</span> к бесконечности функции <span class="arithmatex">\(T(n)\)</span> и <span class="arithmatex">\(f(n)\)</span> имеют один и тот же порядок роста и отличаются только постоянным коэффициентом <span class="arithmatex">\(c\)</span>.</p>
<p><a class="glightbox" href="../time_complexity.assets/asymptotic_upper_bound.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Асимптотическая верхняя граница функции" class="animation-figure" src="../time_complexity.assets/asymptotic_upper_bound.png" /></a></p>
<p align="center"> Рисунок 2-8 &nbsp; Асимптотическая верхняя граница функции </p>
<h2 id="233">2.3.3 &nbsp; Метод вывода<a class="headerlink" href="#233" title="Permanent link">&para;</a></h2>
<p>Математическое определение асимптотической верхней границы выглядит довольно формально, и если ты понял его не до конца, переживать не стоит. Сначала можно освоить сам метод вывода, а в процессе дальнейшей практики постепенно почувствовать его математический смысл.</p>
<p>Согласно определению, после того как мы определили <span class="arithmatex">\(f(n)\)</span> , мы можем получить временную сложность <span class="arithmatex">\(O(f(n))\)</span> . Но как определить саму асимптотическую верхнюю границу <span class="arithmatex">\(f(n)\)</span> ? В целом процесс состоит из двух шагов: сначала подсчитать количество операций, затем определить асимптотическую верхнюю границу.</p>
<h3 id="1-1">1. &nbsp; Шаг 1: подсчет количества операций<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
<p>Для кода это можно делать построчно сверху вниз. Однако, поскольку в выражении <span class="arithmatex">\(c \cdot f(n)\)</span> выше постоянный коэффициент <span class="arithmatex">\(c\)</span> может быть сколь угодно большим, <strong>различные коэффициенты и постоянные члены в числе операций <span class="arithmatex">\(T(n)\)</span> можно игнорировать</strong>. Исходя из этого принципа, можно сформулировать следующие упрощающие приемы подсчета.</p>
<ol>
<li><strong>Игнорировать константы в <span class="arithmatex">\(T(n)\)</span></strong>. Они не зависят от <span class="arithmatex">\(n\)</span> , а значит не влияют на временную сложность.</li>
<li><strong>Опускать все коэффициенты</strong>. Например, циклы на <span class="arithmatex">\(2n\)</span> раз или <span class="arithmatex">\(5n + 1\)</span> раз можно упростить до <span class="arithmatex">\(n\)</span> раз, потому что коэффициент перед <span class="arithmatex">\(n\)</span> не влияет на временную сложность.</li>
<li><strong>При вложенных циклах использовать умножение</strong>. Общее число операций равно произведению числа операций внешнего и внутреннего циклов; при этом для каждого уровня цикла по-прежнему можно применять приемы из пунктов <code>1.</code> и <code>2.</code> .</li>
</ol>
<p>Для заданной функции мы можем использовать перечисленные выше приемы и подсчитать число операций:</p>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># +0 (прием 1)</span>
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">n</span> <span class="c1"># +0 (прием 1)</span>
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a> <span class="c1"># +n (прием 2)</span>
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a> <span class="c1"># +n*n (прием 3)</span>
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="p">):</span>
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a>
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a>
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="c1">// +0 (прием 1)</span>
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="c1">// +n (прием 2)</span>
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="c1">// +n*n (прием 3)</span>
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># +0 (прием 1)</span>
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="c1"># +0 (прием 1)</span>
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="c1"># +n (прием 2)</span>
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="c1"># +n*n (прием 3)</span>
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<p>Следующая формула показывает результаты подсчета до и после использования перечисленных выше приемов; в обоих случаях выводимая временная сложность равна <span class="arithmatex">\(O(n^2)\)</span> .</p>
<div class="arithmatex">\[
\begin{aligned}
T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \text{полный подсчет (-.-|||)} \newline
&amp; = 2n^2 + 7n + 3 \newline
T(n) &amp; = n^2 + n &amp; \text{ленивый подсчет (o.O)}
\end{aligned}
\]</div>
<h3 id="2-2">2. &nbsp; Шаг 2: определение асимптотической верхней границы<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
<p>**Временная сложность определяется старшим по степени членом в <span class="arithmatex">\(T(n)\)</span> **. Это связано с тем, что при стремлении <span class="arithmatex">\(n\)</span> к бесконечности именно старший член начинает доминировать, а влиянием остальных членов можно пренебречь.</p>
<p>В таблице 2-2 приведены несколько примеров. Некоторые значения специально сделаны преувеличенными, чтобы подчеркнуть вывод: "коэффициент не способен изменить порядок". Когда <span class="arithmatex">\(n\)</span> стремится к бесконечности, эти константы становятся несущественными.</p>
<p align="center"> Таблица 2-2 &nbsp; Временная сложность, соответствующая разному количеству операций </p>
<div class="center-table">
<table>
<thead>
<tr>
<th>Число операций <span class="arithmatex">\(T(n)\)</span></th>
<th>Временная сложность <span class="arithmatex">\(O(f(n))\)</span></th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="arithmatex">\(100000\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><span class="arithmatex">\(3n + 2\)</span></td>
<td><span class="arithmatex">\(O(n)\)</span></td>
</tr>
<tr>
<td><span class="arithmatex">\(2n^2 + 3n + 2\)</span></td>
<td><span class="arithmatex">\(O(n^2)\)</span></td>
</tr>
<tr>
<td><span class="arithmatex">\(n^3 + 10000n^2\)</span></td>
<td><span class="arithmatex">\(O(n^3)\)</span></td>
</tr>
<tr>
<td><span class="arithmatex">\(2^n + 10000n^{10000}\)</span></td>
<td><span class="arithmatex">\(O(2^n)\)</span></td>
</tr>
</tbody>
</table>
</div>
<h2 id="234">2.3.4 &nbsp; Распространенные типы<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
<p>Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> ; распространенные типы временной сложности показаны на рисунке 2-9 (в порядке от меньшей к большей).</p>
<div class="arithmatex">\[
\begin{aligned}
O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \newline
\text{Постоянная} &lt; \text{Логарифмическая} &lt; \text{Линейная} &lt; \text{Линейно-логарифмическая} &lt; \text{Квадратичная} &lt; \text{Экспоненциальная} &lt; \text{Факториальная}
\end{aligned}
\]</div>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_common_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Распространенные типы временной сложности" class="animation-figure" src="../time_complexity.assets/time_complexity_common_types.png" /></a></p>
<p align="center"> Рисунок 2-9 &nbsp; Распространенные типы временной сложности </p>
<h3 id="1-o1">1. &nbsp; Постоянная сложность <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
<p>Число операций при постоянной сложности не зависит от размера входных данных <span class="arithmatex">\(n\)</span> , то есть не изменяется вместе с изменением <span class="arithmatex">\(n\)</span> .</p>
<p>В следующей функции, хотя число операций <code>size</code> может быть большим, оно не зависит от размера входных данных <span class="arithmatex">\(n\)</span> , поэтому временная сложность по-прежнему равна <span class="arithmatex">\(O(1)\)</span> :</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Постоянная сложность&quot;&quot;&quot;</span>
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a> <span class="n">size</span> <span class="o">=</span> <span class="mi">100000</span>
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size</span><span class="p">):</span>
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">100_000</span>
<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">100000</span><span class="p">;</span>
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">100000</span><span class="p">;</span>
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">100000</span><span class="p">;</span>
<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100_000</span><span class="p">;</span>
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* Постоянная сложность */</span>
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">100000</span>
<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">)</span>
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">=begin</span>
<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="cm">=end</span>
<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a>
<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a>
<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a>
<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20constant%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20size%20%3D%2010%0A%20%20%20%20for%20_%20in%20range%28size%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20constant%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20constant%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20size%20%3D%2010%0A%20%20%20%20for%20_%20in%20range%28size%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20constant%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<h3 id="2-on">2. &nbsp; Линейная сложность <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
<p>Число операций при линейной сложности растет линейно относительно размера входных данных <span class="arithmatex">\(n\)</span> . Линейная сложность обычно встречается в одноуровневых циклах:</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Линейная сложность&quot;&quot;&quot;</span>
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* Линейная сложность */</span>
<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">=begin</span>
<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="cm">=end</span>
<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a>
<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a>
<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></a>
<a id="__codelineno-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-77-15" name="__codelineno-77-15" href="#__codelineno-77-15"></a><span class="k">end</span>
<a id="__codelineno-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></a>
<a id="__codelineno-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-77-18" name="__codelineno-77-18" href="#__codelineno-77-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-77-19" name="__codelineno-77-19" href="#__codelineno-77-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-77-20" name="__codelineno-77-20" href="#__codelineno-77-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-77-21" name="__codelineno-77-21" href="#__codelineno-77-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-77-22" name="__codelineno-77-22" href="#__codelineno-77-22"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p>Операции обхода массива и обхода связного списка имеют временную сложность <span class="arithmatex">\(O(n)\)</span> , где <span class="arithmatex">\(n\)</span> - длина массива или списка:</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Линейная сложность (обход массива)&quot;&quot;&quot;</span>
<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a> <span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
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<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="p">}</span>
</code></pre></div>
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<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="p">}</span>
</code></pre></div>
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<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ArrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="p">}</span>
</code></pre></div>
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<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="p">}</span>
</code></pre></div>
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<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">arrayTraversal</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* Линейная сложность (обход массива) */</span>
<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w"> </span><span class="c1">// Число итераций пропорционально длине массива</span>
<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">=begin</span>
<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="cm">=end</span>
<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a>
<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a>
<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a>
<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="k">end</span>
<a id="__codelineno-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></a>
<a id="__codelineno-90-17" name="__codelineno-90-17" href="#__codelineno-90-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-90-18" name="__codelineno-90-18" href="#__codelineno-90-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-90-19" name="__codelineno-90-19" href="#__codelineno-90-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-90-20" name="__codelineno-90-20" href="#__codelineno-90-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-90-21" name="__codelineno-90-21" href="#__codelineno-90-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-90-22" name="__codelineno-90-22" href="#__codelineno-90-22"></a><span class="k">end</span>
<a id="__codelineno-90-23" name="__codelineno-90-23" href="#__codelineno-90-23"></a>
<a id="__codelineno-90-24" name="__codelineno-90-24" href="#__codelineno-90-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-90-25" name="__codelineno-90-25" href="#__codelineno-90-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-90-26" name="__codelineno-90-26" href="#__codelineno-90-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-90-27" name="__codelineno-90-27" href="#__codelineno-90-27"></a>
<a id="__codelineno-90-28" name="__codelineno-90-28" href="#__codelineno-90-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-90-29" name="__codelineno-90-29" href="#__codelineno-90-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-90-30" name="__codelineno-90-30" href="#__codelineno-90-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-90-31" name="__codelineno-90-31" href="#__codelineno-90-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-90-32" name="__codelineno-90-32" href="#__codelineno-90-32"></a>
<a id="__codelineno-90-33" name="__codelineno-90-33" href="#__codelineno-90-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-90-34" name="__codelineno-90-34" href="#__codelineno-90-34"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20array_traversal%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BF%D1%80%D0%BE%D0%BF%D0%BE%D1%80%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%20%D0%B4%D0%BB%D0%B8%D0%BD%D0%B5%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20array_traversal%28%5B0%5D%20%2A%20n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20array_traversal%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BF%D1%80%D0%BE%D0%BF%D0%BE%D1%80%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%20%D0%B4%D0%BB%D0%B8%D0%BD%D0%B5%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20array_traversal%28%5B0%5D%20%2A%20n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p>Стоит отметить, что <strong>размер входных данных <span class="arithmatex">\(n\)</span> нужно определять конкретно в зависимости от типа входа</strong>. Например, в первом примере переменная <span class="arithmatex">\(n\)</span> сама является размером входных данных; во втором примере размером данных служит длина массива <span class="arithmatex">\(n\)</span> .</p>
<h3 id="3-on2">3. &nbsp; Квадратичная сложность <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
<p>Число операций при квадратичной сложности растет квадратично относительно размера входных данных <span class="arithmatex">\(n\)</span> . Квадратичная сложность обычно встречается во вложенных циклах: временная сложность внешнего и внутреннего циклов равна <span class="arithmatex">\(O(n)\)</span> , поэтому общая временная сложность составляет <span class="arithmatex">\(O(n^2)\)</span> :</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Квадратичная сложность&quot;&quot;&quot;</span>
<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a> <span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-97-10" name="__codelineno-97-10" href="#__codelineno-97-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* Квадратичная сложность */</span>
<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w"> </span><span class="c1">// Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="cm">=begin</span>
<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a><span class="cm">=end</span>
<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a>
<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a>
<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a>
<a id="__codelineno-103-14" name="__codelineno-103-14" href="#__codelineno-103-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-103-15" name="__codelineno-103-15" href="#__codelineno-103-15"></a><span class="k">end</span>
<a id="__codelineno-103-16" name="__codelineno-103-16" href="#__codelineno-103-16"></a>
<a id="__codelineno-103-17" name="__codelineno-103-17" href="#__codelineno-103-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-103-18" name="__codelineno-103-18" href="#__codelineno-103-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-103-19" name="__codelineno-103-19" href="#__codelineno-103-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-103-20" name="__codelineno-103-20" href="#__codelineno-103-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-103-21" name="__codelineno-103-21" href="#__codelineno-103-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-103-22" name="__codelineno-103-22" href="#__codelineno-103-22"></a><span class="k">end</span>
<a id="__codelineno-103-23" name="__codelineno-103-23" href="#__codelineno-103-23"></a>
<a id="__codelineno-103-24" name="__codelineno-103-24" href="#__codelineno-103-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-103-25" name="__codelineno-103-25" href="#__codelineno-103-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-103-26" name="__codelineno-103-26" href="#__codelineno-103-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-103-27" name="__codelineno-103-27" href="#__codelineno-103-27"></a>
<a id="__codelineno-103-28" name="__codelineno-103-28" href="#__codelineno-103-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-103-29" name="__codelineno-103-29" href="#__codelineno-103-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-103-30" name="__codelineno-103-30" href="#__codelineno-103-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-103-31" name="__codelineno-103-31" href="#__codelineno-103-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-103-32" name="__codelineno-103-32" href="#__codelineno-103-32"></a>
<a id="__codelineno-103-33" name="__codelineno-103-33" href="#__codelineno-103-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-103-34" name="__codelineno-103-34" href="#__codelineno-103-34"></a><span class="k">end</span>
<a id="__codelineno-103-35" name="__codelineno-103-35" href="#__codelineno-103-35"></a>
<a id="__codelineno-103-36" name="__codelineno-103-36" href="#__codelineno-103-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-103-37" name="__codelineno-103-37" href="#__codelineno-103-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-103-38" name="__codelineno-103-38" href="#__codelineno-103-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-103-39" name="__codelineno-103-39" href="#__codelineno-103-39"></a>
<a id="__codelineno-103-40" name="__codelineno-103-40" href="#__codelineno-103-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-103-41" name="__codelineno-103-41" href="#__codelineno-103-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-103-42" name="__codelineno-103-42" href="#__codelineno-103-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-103-43" name="__codelineno-103-43" href="#__codelineno-103-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-103-44" name="__codelineno-103-44" href="#__codelineno-103-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-103-45" name="__codelineno-103-45" href="#__codelineno-103-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-103-46" name="__codelineno-103-46" href="#__codelineno-103-46"></a>
<a id="__codelineno-103-47" name="__codelineno-103-47" href="#__codelineno-103-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-103-48" name="__codelineno-103-48" href="#__codelineno-103-48"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE%20%D0%B7%D0%B0%D0%B2%D0%B8%D1%81%D0%B8%D1%82%20%D0%BE%D1%82%20%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%B0%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE%20%D0%B7%D0%B0%D0%B2%D0%B8%D1%81%D0%B8%D1%82%20%D0%BE%D1%82%20%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%B0%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p>На рисунке 2-10 сравниваются три временные сложности: постоянная, линейная и квадратичная.</p>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Постоянная, линейная и квадратичная временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></a></p>
<p align="center"> Рисунок 2-10 &nbsp; Постоянная, линейная и квадратичная временная сложность </p>
<p>Возьмем в качестве примера пузырьковую сортировку: внешний цикл выполняется <span class="arithmatex">\(n - 1\)</span> раз, внутренний цикл выполняется <span class="arithmatex">\(n-1\)</span> , <span class="arithmatex">\(n-2\)</span> , <span class="arithmatex">\(\dots\)</span> , <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(1\)</span> раз, в среднем это <span class="arithmatex">\(n / 2\)</span> раз, поэтому временная сложность равна <span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span> :</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Квадратичная сложность (пузырьковая сортировка)&quot;&quot;&quot;</span>
<a id="__codelineno-104-3" name="__codelineno-104-3" href="#__codelineno-104-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># Счетчик</span>
<a id="__codelineno-104-4" name="__codelineno-104-4" href="#__codelineno-104-4"></a> <span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-104-5" name="__codelineno-104-5" href="#__codelineno-104-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<a id="__codelineno-104-6" name="__codelineno-104-6" href="#__codelineno-104-6"></a> <span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-104-7" name="__codelineno-104-7" href="#__codelineno-104-7"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<a id="__codelineno-104-8" name="__codelineno-104-8" href="#__codelineno-104-8"></a> <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
<a id="__codelineno-104-9" name="__codelineno-104-9" href="#__codelineno-104-9"></a> <span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-104-10" name="__codelineno-104-10" href="#__codelineno-104-10"></a> <span class="n">tmp</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<a id="__codelineno-104-11" name="__codelineno-104-11" href="#__codelineno-104-11"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-104-12" name="__codelineno-104-12" href="#__codelineno-104-12"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
<a id="__codelineno-104-13" name="__codelineno-104-13" href="#__codelineno-104-13"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">3</span> <span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-104-14" name="__codelineno-104-14" href="#__codelineno-104-14"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-105-4" name="__codelineno-105-4" href="#__codelineno-105-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-105-5" name="__codelineno-105-5" href="#__codelineno-105-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-105-6" name="__codelineno-105-6" href="#__codelineno-105-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-105-7" name="__codelineno-105-7" href="#__codelineno-105-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-105-8" name="__codelineno-105-8" href="#__codelineno-105-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-105-9" name="__codelineno-105-9" href="#__codelineno-105-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-105-10" name="__codelineno-105-10" href="#__codelineno-105-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a id="__codelineno-105-11" name="__codelineno-105-11" href="#__codelineno-105-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a id="__codelineno-105-12" name="__codelineno-105-12" href="#__codelineno-105-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
<a id="__codelineno-105-13" name="__codelineno-105-13" href="#__codelineno-105-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-105-14" name="__codelineno-105-14" href="#__codelineno-105-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-105-15" name="__codelineno-105-15" href="#__codelineno-105-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-105-16" name="__codelineno-105-16" href="#__codelineno-105-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-105-17" name="__codelineno-105-17" href="#__codelineno-105-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-105-18" name="__codelineno-105-18" href="#__codelineno-105-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-106-3" name="__codelineno-106-3" href="#__codelineno-106-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-106-4" name="__codelineno-106-4" href="#__codelineno-106-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-106-5" name="__codelineno-106-5" href="#__codelineno-106-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-106-6" name="__codelineno-106-6" href="#__codelineno-106-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-106-7" name="__codelineno-106-7" href="#__codelineno-106-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-106-8" name="__codelineno-106-8" href="#__codelineno-106-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-106-9" name="__codelineno-106-9" href="#__codelineno-106-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-106-10" name="__codelineno-106-10" href="#__codelineno-106-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
<a id="__codelineno-106-11" name="__codelineno-106-11" href="#__codelineno-106-11"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
<a id="__codelineno-106-12" name="__codelineno-106-12" href="#__codelineno-106-12"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
<a id="__codelineno-106-13" name="__codelineno-106-13" href="#__codelineno-106-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-106-14" name="__codelineno-106-14" href="#__codelineno-106-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-106-15" name="__codelineno-106-15" href="#__codelineno-106-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-106-16" name="__codelineno-106-16" href="#__codelineno-106-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-106-17" name="__codelineno-106-17" href="#__codelineno-106-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-106-18" name="__codelineno-106-18" href="#__codelineno-106-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-107-3" name="__codelineno-107-3" href="#__codelineno-107-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-107-4" name="__codelineno-107-4" href="#__codelineno-107-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-107-5" name="__codelineno-107-5" href="#__codelineno-107-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-107-6" name="__codelineno-107-6" href="#__codelineno-107-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-107-7" name="__codelineno-107-7" href="#__codelineno-107-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-107-8" name="__codelineno-107-8" href="#__codelineno-107-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-107-9" name="__codelineno-107-9" href="#__codelineno-107-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-107-10" name="__codelineno-107-10" href="#__codelineno-107-10"></a><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
<a id="__codelineno-107-11" name="__codelineno-107-11" href="#__codelineno-107-11"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-107-12" name="__codelineno-107-12" href="#__codelineno-107-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-107-13" name="__codelineno-107-13" href="#__codelineno-107-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-107-14" name="__codelineno-107-14" href="#__codelineno-107-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-107-15" name="__codelineno-107-15" href="#__codelineno-107-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-107-16" name="__codelineno-107-16" href="#__codelineno-107-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-108-4" name="__codelineno-108-4" href="#__codelineno-108-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-108-9" name="__codelineno-108-9" href="#__codelineno-108-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-108-11" name="__codelineno-108-11" href="#__codelineno-108-11"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-108-12" name="__codelineno-108-12" href="#__codelineno-108-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span>
<a id="__codelineno-108-13" name="__codelineno-108-13" href="#__codelineno-108-13"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-108-14" name="__codelineno-108-14" href="#__codelineno-108-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-108-15" name="__codelineno-108-15" href="#__codelineno-108-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-108-16" name="__codelineno-108-16" href="#__codelineno-108-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-108-17" name="__codelineno-108-17" href="#__codelineno-108-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-108-18" name="__codelineno-108-18" href="#__codelineno-108-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">().</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-109-10" name="__codelineno-109-10" href="#__codelineno-109-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<a id="__codelineno-109-11" name="__codelineno-109-11" href="#__codelineno-109-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-109-12" name="__codelineno-109-12" href="#__codelineno-109-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-109-13" name="__codelineno-109-13" href="#__codelineno-109-13"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-109-14" name="__codelineno-109-14" href="#__codelineno-109-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-109-15" name="__codelineno-109-15" href="#__codelineno-109-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-109-16" name="__codelineno-109-16" href="#__codelineno-109-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-109-17" name="__codelineno-109-17" href="#__codelineno-109-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-109-18" name="__codelineno-109-18" href="#__codelineno-109-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-110-14" name="__codelineno-110-14" href="#__codelineno-110-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-110-15" name="__codelineno-110-15" href="#__codelineno-110-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-110-16" name="__codelineno-110-16" href="#__codelineno-110-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-110-17" name="__codelineno-110-17" href="#__codelineno-110-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-110-18" name="__codelineno-110-18" href="#__codelineno-110-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-111-8" name="__codelineno-111-8" href="#__codelineno-111-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-111-9" name="__codelineno-111-9" href="#__codelineno-111-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-111-10" name="__codelineno-111-10" href="#__codelineno-111-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
<a id="__codelineno-111-11" name="__codelineno-111-11" href="#__codelineno-111-11"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
<a id="__codelineno-111-12" name="__codelineno-111-12" href="#__codelineno-111-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
<a id="__codelineno-111-13" name="__codelineno-111-13" href="#__codelineno-111-13"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-111-14" name="__codelineno-111-14" href="#__codelineno-111-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-111-15" name="__codelineno-111-15" href="#__codelineno-111-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-111-16" name="__codelineno-111-16" href="#__codelineno-111-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-111-17" name="__codelineno-111-17" href="#__codelineno-111-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-111-18" name="__codelineno-111-18" href="#__codelineno-111-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">bubbleSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-112-3" name="__codelineno-112-3" href="#__codelineno-112-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-112-4" name="__codelineno-112-4" href="#__codelineno-112-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-112-5" name="__codelineno-112-5" href="#__codelineno-112-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-112-6" name="__codelineno-112-6" href="#__codelineno-112-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-112-7" name="__codelineno-112-7" href="#__codelineno-112-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-112-8" name="__codelineno-112-8" href="#__codelineno-112-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-112-9" name="__codelineno-112-9" href="#__codelineno-112-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-112-10" name="__codelineno-112-10" href="#__codelineno-112-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a id="__codelineno-112-11" name="__codelineno-112-11" href="#__codelineno-112-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
<a id="__codelineno-112-12" name="__codelineno-112-12" href="#__codelineno-112-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
<a id="__codelineno-112-13" name="__codelineno-112-13" href="#__codelineno-112-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-112-14" name="__codelineno-112-14" href="#__codelineno-112-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-112-15" name="__codelineno-112-15" href="#__codelineno-112-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-112-16" name="__codelineno-112-16" href="#__codelineno-112-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-112-17" name="__codelineno-112-17" href="#__codelineno-112-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-112-18" name="__codelineno-112-18" href="#__codelineno-112-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-113-2" name="__codelineno-113-2" href="#__codelineno-113-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-113-3" name="__codelineno-113-3" href="#__codelineno-113-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-113-4" name="__codelineno-113-4" href="#__codelineno-113-4"></a>
<a id="__codelineno-113-5" name="__codelineno-113-5" href="#__codelineno-113-5"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-113-6" name="__codelineno-113-6" href="#__codelineno-113-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-113-7" name="__codelineno-113-7" href="#__codelineno-113-7"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-113-8" name="__codelineno-113-8" href="#__codelineno-113-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-113-9" name="__codelineno-113-9" href="#__codelineno-113-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-113-10" name="__codelineno-113-10" href="#__codelineno-113-10"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-113-11" name="__codelineno-113-11" href="#__codelineno-113-11"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a id="__codelineno-113-12" name="__codelineno-113-12" href="#__codelineno-113-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a id="__codelineno-113-13" name="__codelineno-113-13" href="#__codelineno-113-13"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
<a id="__codelineno-113-14" name="__codelineno-113-14" href="#__codelineno-113-14"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-113-15" name="__codelineno-113-15" href="#__codelineno-113-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-113-16" name="__codelineno-113-16" href="#__codelineno-113-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-113-17" name="__codelineno-113-17" href="#__codelineno-113-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-113-18" name="__codelineno-113-18" href="#__codelineno-113-18"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-113-19" name="__codelineno-113-19" href="#__codelineno-113-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-114-2" name="__codelineno-114-2" href="#__codelineno-114-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-114-3" name="__codelineno-114-3" href="#__codelineno-114-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-114-4" name="__codelineno-114-4" href="#__codelineno-114-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-114-5" name="__codelineno-114-5" href="#__codelineno-114-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-114-6" name="__codelineno-114-6" href="#__codelineno-114-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-114-7" name="__codelineno-114-7" href="#__codelineno-114-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-114-8" name="__codelineno-114-8" href="#__codelineno-114-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-114-9" name="__codelineno-114-9" href="#__codelineno-114-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-114-10" name="__codelineno-114-10" href="#__codelineno-114-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a id="__codelineno-114-11" name="__codelineno-114-11" href="#__codelineno-114-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a id="__codelineno-114-12" name="__codelineno-114-12" href="#__codelineno-114-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
<a id="__codelineno-114-13" name="__codelineno-114-13" href="#__codelineno-114-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-114-14" name="__codelineno-114-14" href="#__codelineno-114-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-114-15" name="__codelineno-114-15" href="#__codelineno-114-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-114-16" name="__codelineno-114-16" href="#__codelineno-114-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-114-17" name="__codelineno-114-17" href="#__codelineno-114-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-114-18" name="__codelineno-114-18" href="#__codelineno-114-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="cm">/* Квадратичная сложность (пузырьковая сортировка) */</span>
<a id="__codelineno-115-2" name="__codelineno-115-2" href="#__codelineno-115-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-115-3" name="__codelineno-115-3" href="#__codelineno-115-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// Счетчик</span>
<a id="__codelineno-115-4" name="__codelineno-115-4" href="#__codelineno-115-4"></a><span class="w"> </span><span class="c1">// Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-115-5" name="__codelineno-115-5" href="#__codelineno-115-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-115-6" name="__codelineno-115-6" href="#__codelineno-115-6"></a><span class="w"> </span><span class="c1">// Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-115-7" name="__codelineno-115-7" href="#__codelineno-115-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-115-8" name="__codelineno-115-8" href="#__codelineno-115-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-115-9" name="__codelineno-115-9" href="#__codelineno-115-9"></a><span class="w"> </span><span class="c1">// Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-115-10" name="__codelineno-115-10" href="#__codelineno-115-10"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-115-11" name="__codelineno-115-11" href="#__codelineno-115-11"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
<a id="__codelineno-115-12" name="__codelineno-115-12" href="#__codelineno-115-12"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
<a id="__codelineno-115-13" name="__codelineno-115-13" href="#__codelineno-115-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="c1">// Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-115-14" name="__codelineno-115-14" href="#__codelineno-115-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-115-15" name="__codelineno-115-15" href="#__codelineno-115-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-115-16" name="__codelineno-115-16" href="#__codelineno-115-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-115-17" name="__codelineno-115-17" href="#__codelineno-115-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-115-18" name="__codelineno-115-18" href="#__codelineno-115-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="cm">=begin</span>
<a id="__codelineno-116-2" name="__codelineno-116-2" href="#__codelineno-116-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-116-3" name="__codelineno-116-3" href="#__codelineno-116-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-116-4" name="__codelineno-116-4" href="#__codelineno-116-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-116-5" name="__codelineno-116-5" href="#__codelineno-116-5"></a><span class="cm">=end</span>
<a id="__codelineno-116-6" name="__codelineno-116-6" href="#__codelineno-116-6"></a>
<a id="__codelineno-116-7" name="__codelineno-116-7" href="#__codelineno-116-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-116-8" name="__codelineno-116-8" href="#__codelineno-116-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-116-9" name="__codelineno-116-9" href="#__codelineno-116-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-116-10" name="__codelineno-116-10" href="#__codelineno-116-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-116-11" name="__codelineno-116-11" href="#__codelineno-116-11"></a>
<a id="__codelineno-116-12" name="__codelineno-116-12" href="#__codelineno-116-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-116-13" name="__codelineno-116-13" href="#__codelineno-116-13"></a>
<a id="__codelineno-116-14" name="__codelineno-116-14" href="#__codelineno-116-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-116-15" name="__codelineno-116-15" href="#__codelineno-116-15"></a><span class="k">end</span>
<a id="__codelineno-116-16" name="__codelineno-116-16" href="#__codelineno-116-16"></a>
<a id="__codelineno-116-17" name="__codelineno-116-17" href="#__codelineno-116-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-116-18" name="__codelineno-116-18" href="#__codelineno-116-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-116-19" name="__codelineno-116-19" href="#__codelineno-116-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-116-20" name="__codelineno-116-20" href="#__codelineno-116-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-116-21" name="__codelineno-116-21" href="#__codelineno-116-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-116-22" name="__codelineno-116-22" href="#__codelineno-116-22"></a><span class="k">end</span>
<a id="__codelineno-116-23" name="__codelineno-116-23" href="#__codelineno-116-23"></a>
<a id="__codelineno-116-24" name="__codelineno-116-24" href="#__codelineno-116-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-116-25" name="__codelineno-116-25" href="#__codelineno-116-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-116-26" name="__codelineno-116-26" href="#__codelineno-116-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-116-27" name="__codelineno-116-27" href="#__codelineno-116-27"></a>
<a id="__codelineno-116-28" name="__codelineno-116-28" href="#__codelineno-116-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-116-29" name="__codelineno-116-29" href="#__codelineno-116-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-116-30" name="__codelineno-116-30" href="#__codelineno-116-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-116-31" name="__codelineno-116-31" href="#__codelineno-116-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-116-32" name="__codelineno-116-32" href="#__codelineno-116-32"></a>
<a id="__codelineno-116-33" name="__codelineno-116-33" href="#__codelineno-116-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-116-34" name="__codelineno-116-34" href="#__codelineno-116-34"></a><span class="k">end</span>
<a id="__codelineno-116-35" name="__codelineno-116-35" href="#__codelineno-116-35"></a>
<a id="__codelineno-116-36" name="__codelineno-116-36" href="#__codelineno-116-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-116-37" name="__codelineno-116-37" href="#__codelineno-116-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-116-38" name="__codelineno-116-38" href="#__codelineno-116-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-116-39" name="__codelineno-116-39" href="#__codelineno-116-39"></a>
<a id="__codelineno-116-40" name="__codelineno-116-40" href="#__codelineno-116-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-116-41" name="__codelineno-116-41" href="#__codelineno-116-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-116-42" name="__codelineno-116-42" href="#__codelineno-116-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-116-43" name="__codelineno-116-43" href="#__codelineno-116-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-116-44" name="__codelineno-116-44" href="#__codelineno-116-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-116-45" name="__codelineno-116-45" href="#__codelineno-116-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-116-46" name="__codelineno-116-46" href="#__codelineno-116-46"></a>
<a id="__codelineno-116-47" name="__codelineno-116-47" href="#__codelineno-116-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-116-48" name="__codelineno-116-48" href="#__codelineno-116-48"></a><span class="k">end</span>
<a id="__codelineno-116-49" name="__codelineno-116-49" href="#__codelineno-116-49"></a>
<a id="__codelineno-116-50" name="__codelineno-116-50" href="#__codelineno-116-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-116-51" name="__codelineno-116-51" href="#__codelineno-116-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-116-52" name="__codelineno-116-52" href="#__codelineno-116-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-116-53" name="__codelineno-116-53" href="#__codelineno-116-53"></a>
<a id="__codelineno-116-54" name="__codelineno-116-54" href="#__codelineno-116-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-116-55" name="__codelineno-116-55" href="#__codelineno-116-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-116-56" name="__codelineno-116-56" href="#__codelineno-116-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-116-57" name="__codelineno-116-57" href="#__codelineno-116-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-116-58" name="__codelineno-116-58" href="#__codelineno-116-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-116-59" name="__codelineno-116-59" href="#__codelineno-116-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-116-60" name="__codelineno-116-60" href="#__codelineno-116-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-116-61" name="__codelineno-116-61" href="#__codelineno-116-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-116-62" name="__codelineno-116-62" href="#__codelineno-116-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-116-63" name="__codelineno-116-63" href="#__codelineno-116-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-116-64" name="__codelineno-116-64" href="#__codelineno-116-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-116-65" name="__codelineno-116-65" href="#__codelineno-116-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-116-66" name="__codelineno-116-66" href="#__codelineno-116-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-116-67" name="__codelineno-116-67" href="#__codelineno-116-67"></a>
<a id="__codelineno-116-68" name="__codelineno-116-68" href="#__codelineno-116-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-116-69" name="__codelineno-116-69" href="#__codelineno-116-69"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
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</details>
<h3 id="4-o2n">4. &nbsp; Экспоненциальная сложность <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
<p>Типичный пример экспоненциального роста в биологии - "деление клеток": в начальном состоянии есть 1 клетка, после одного деления их становится 2, после двух делений - 4 и так далее; после <span class="arithmatex">\(n\)</span> раундов деления клеток становится <span class="arithmatex">\(2^n\)</span> .</p>
<p>На рисунке 2-11 и в следующем коде моделируется процесс деления клеток; временная сложность равна <span class="arithmatex">\(O(2^n)\)</span> . Обрати внимание, что входное значение <span class="arithmatex">\(n\)</span> обозначает число раундов деления, а возвращаемое значение <code>count</code> обозначает общее число делений.</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-117-2" name="__codelineno-117-2" href="#__codelineno-117-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Экспоненциальная сложность (итеративная реализация)&quot;&quot;&quot;</span>
<a id="__codelineno-117-3" name="__codelineno-117-3" href="#__codelineno-117-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-117-4" name="__codelineno-117-4" href="#__codelineno-117-4"></a> <span class="n">base</span> <span class="o">=</span> <span class="mi">1</span>
<a id="__codelineno-117-5" name="__codelineno-117-5" href="#__codelineno-117-5"></a> <span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-117-6" name="__codelineno-117-6" href="#__codelineno-117-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-117-7" name="__codelineno-117-7" href="#__codelineno-117-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">base</span><span class="p">):</span>
<a id="__codelineno-117-8" name="__codelineno-117-8" href="#__codelineno-117-8"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-117-9" name="__codelineno-117-9" href="#__codelineno-117-9"></a> <span class="n">base</span> <span class="o">*=</span> <span class="mi">2</span>
<a id="__codelineno-117-10" name="__codelineno-117-10" href="#__codelineno-117-10"></a> <span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-117-11" name="__codelineno-117-11" href="#__codelineno-117-11"></a> <span class="k">return</span> <span class="n">count</span>
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<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-118-2" name="__codelineno-118-2" href="#__codelineno-118-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-118-3" name="__codelineno-118-3" href="#__codelineno-118-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-118-4" name="__codelineno-118-4" href="#__codelineno-118-4"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-118-5" name="__codelineno-118-5" href="#__codelineno-118-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-118-6" name="__codelineno-118-6" href="#__codelineno-118-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-118-7" name="__codelineno-118-7" href="#__codelineno-118-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-118-8" name="__codelineno-118-8" href="#__codelineno-118-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-118-9" name="__codelineno-118-9" href="#__codelineno-118-9"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-118-10" name="__codelineno-118-10" href="#__codelineno-118-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-118-11" name="__codelineno-118-11" href="#__codelineno-118-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-118-12" name="__codelineno-118-12" href="#__codelineno-118-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-118-13" name="__codelineno-118-13" href="#__codelineno-118-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-119-5" name="__codelineno-119-5" href="#__codelineno-119-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-119-9" name="__codelineno-119-9" href="#__codelineno-119-9"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-119-12" name="__codelineno-119-12" href="#__codelineno-119-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-119-13" name="__codelineno-119-13" href="#__codelineno-119-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-120-2" name="__codelineno-120-2" href="#__codelineno-120-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-120-3" name="__codelineno-120-3" href="#__codelineno-120-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-120-4" name="__codelineno-120-4" href="#__codelineno-120-4"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-120-5" name="__codelineno-120-5" href="#__codelineno-120-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-120-6" name="__codelineno-120-6" href="#__codelineno-120-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-120-7" name="__codelineno-120-7" href="#__codelineno-120-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-120-8" name="__codelineno-120-8" href="#__codelineno-120-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-120-9" name="__codelineno-120-9" href="#__codelineno-120-9"></a><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-120-10" name="__codelineno-120-10" href="#__codelineno-120-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-120-11" name="__codelineno-120-11" href="#__codelineno-120-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-120-12" name="__codelineno-120-12" href="#__codelineno-120-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-120-13" name="__codelineno-120-13" href="#__codelineno-120-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-121-2" name="__codelineno-121-2" href="#__codelineno-121-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-121-3" name="__codelineno-121-3" href="#__codelineno-121-3"></a><span class="w"> </span><span class="nx">count</span><span class="p">,</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-121-4" name="__codelineno-121-4" href="#__codelineno-121-4"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-121-5" name="__codelineno-121-5" href="#__codelineno-121-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-121-6" name="__codelineno-121-6" href="#__codelineno-121-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-121-7" name="__codelineno-121-7" href="#__codelineno-121-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-121-8" name="__codelineno-121-8" href="#__codelineno-121-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-121-9" name="__codelineno-121-9" href="#__codelineno-121-9"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-121-10" name="__codelineno-121-10" href="#__codelineno-121-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-121-11" name="__codelineno-121-11" href="#__codelineno-121-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-121-12" name="__codelineno-121-12" href="#__codelineno-121-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-121-13" name="__codelineno-121-13" href="#__codelineno-121-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-122-3" name="__codelineno-122-3" href="#__codelineno-122-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-122-4" name="__codelineno-122-4" href="#__codelineno-122-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">base</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-122-5" name="__codelineno-122-5" href="#__codelineno-122-5"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-122-6" name="__codelineno-122-6" href="#__codelineno-122-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-122-7" name="__codelineno-122-7" href="#__codelineno-122-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-122-8" name="__codelineno-122-8" href="#__codelineno-122-8"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-122-9" name="__codelineno-122-9" href="#__codelineno-122-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-122-10" name="__codelineno-122-10" href="#__codelineno-122-10"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-122-11" name="__codelineno-122-11" href="#__codelineno-122-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-122-12" name="__codelineno-122-12" href="#__codelineno-122-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-122-13" name="__codelineno-122-13" href="#__codelineno-122-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-122-14" name="__codelineno-122-14" href="#__codelineno-122-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-123-1" name="__codelineno-123-1" href="#__codelineno-123-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-123-2" name="__codelineno-123-2" href="#__codelineno-123-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-123-3" name="__codelineno-123-3" href="#__codelineno-123-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
<a id="__codelineno-123-4" name="__codelineno-123-4" href="#__codelineno-123-4"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-123-5" name="__codelineno-123-5" href="#__codelineno-123-5"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-123-6" name="__codelineno-123-6" href="#__codelineno-123-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-123-7" name="__codelineno-123-7" href="#__codelineno-123-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-123-8" name="__codelineno-123-8" href="#__codelineno-123-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-123-9" name="__codelineno-123-9" href="#__codelineno-123-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-123-10" name="__codelineno-123-10" href="#__codelineno-123-10"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a id="__codelineno-123-11" name="__codelineno-123-11" href="#__codelineno-123-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-123-12" name="__codelineno-123-12" href="#__codelineno-123-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-123-13" name="__codelineno-123-13" href="#__codelineno-123-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-123-14" name="__codelineno-123-14" href="#__codelineno-123-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-124-1" name="__codelineno-124-1" href="#__codelineno-124-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-124-2" name="__codelineno-124-2" href="#__codelineno-124-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-124-3" name="__codelineno-124-3" href="#__codelineno-124-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
<a id="__codelineno-124-4" name="__codelineno-124-4" href="#__codelineno-124-4"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-124-5" name="__codelineno-124-5" href="#__codelineno-124-5"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-124-6" name="__codelineno-124-6" href="#__codelineno-124-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-124-7" name="__codelineno-124-7" href="#__codelineno-124-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-124-8" name="__codelineno-124-8" href="#__codelineno-124-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-124-9" name="__codelineno-124-9" href="#__codelineno-124-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-124-10" name="__codelineno-124-10" href="#__codelineno-124-10"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a id="__codelineno-124-11" name="__codelineno-124-11" href="#__codelineno-124-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-124-12" name="__codelineno-124-12" href="#__codelineno-124-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-124-13" name="__codelineno-124-13" href="#__codelineno-124-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-124-14" name="__codelineno-124-14" href="#__codelineno-124-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-125-1" name="__codelineno-125-1" href="#__codelineno-125-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-125-2" name="__codelineno-125-2" href="#__codelineno-125-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-125-3" name="__codelineno-125-3" href="#__codelineno-125-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-125-4" name="__codelineno-125-4" href="#__codelineno-125-4"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-125-5" name="__codelineno-125-5" href="#__codelineno-125-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-125-6" name="__codelineno-125-6" href="#__codelineno-125-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-125-7" name="__codelineno-125-7" href="#__codelineno-125-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-125-8" name="__codelineno-125-8" href="#__codelineno-125-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-125-9" name="__codelineno-125-9" href="#__codelineno-125-9"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
<a id="__codelineno-125-10" name="__codelineno-125-10" href="#__codelineno-125-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-125-11" name="__codelineno-125-11" href="#__codelineno-125-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-125-12" name="__codelineno-125-12" href="#__codelineno-125-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-125-13" name="__codelineno-125-13" href="#__codelineno-125-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-126-1" name="__codelineno-126-1" href="#__codelineno-126-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-126-2" name="__codelineno-126-2" href="#__codelineno-126-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-126-3" name="__codelineno-126-3" href="#__codelineno-126-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-126-4" name="__codelineno-126-4" href="#__codelineno-126-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-126-5" name="__codelineno-126-5" href="#__codelineno-126-5"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-126-6" name="__codelineno-126-6" href="#__codelineno-126-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-126-7" name="__codelineno-126-7" href="#__codelineno-126-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-126-8" name="__codelineno-126-8" href="#__codelineno-126-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-126-9" name="__codelineno-126-9" href="#__codelineno-126-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-126-10" name="__codelineno-126-10" href="#__codelineno-126-10"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-126-11" name="__codelineno-126-11" href="#__codelineno-126-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-126-12" name="__codelineno-126-12" href="#__codelineno-126-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-126-13" name="__codelineno-126-13" href="#__codelineno-126-13"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-126-14" name="__codelineno-126-14" href="#__codelineno-126-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-127-1" name="__codelineno-127-1" href="#__codelineno-127-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-127-2" name="__codelineno-127-2" href="#__codelineno-127-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-127-3" name="__codelineno-127-3" href="#__codelineno-127-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-127-4" name="__codelineno-127-4" href="#__codelineno-127-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-127-5" name="__codelineno-127-5" href="#__codelineno-127-5"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-127-6" name="__codelineno-127-6" href="#__codelineno-127-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-127-7" name="__codelineno-127-7" href="#__codelineno-127-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-127-8" name="__codelineno-127-8" href="#__codelineno-127-8"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-127-9" name="__codelineno-127-9" href="#__codelineno-127-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-127-10" name="__codelineno-127-10" href="#__codelineno-127-10"></a><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-127-11" name="__codelineno-127-11" href="#__codelineno-127-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-127-12" name="__codelineno-127-12" href="#__codelineno-127-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-127-13" name="__codelineno-127-13" href="#__codelineno-127-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-127-14" name="__codelineno-127-14" href="#__codelineno-127-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-128-1" name="__codelineno-128-1" href="#__codelineno-128-1"></a><span class="cm">/* Экспоненциальная сложность (итеративная реализация) */</span>
<a id="__codelineno-128-2" name="__codelineno-128-2" href="#__codelineno-128-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-128-3" name="__codelineno-128-3" href="#__codelineno-128-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-128-4" name="__codelineno-128-4" href="#__codelineno-128-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-128-5" name="__codelineno-128-5" href="#__codelineno-128-5"></a><span class="w"> </span><span class="c1">// На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-128-6" name="__codelineno-128-6" href="#__codelineno-128-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-128-7" name="__codelineno-128-7" href="#__codelineno-128-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-128-8" name="__codelineno-128-8" href="#__codelineno-128-8"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-128-9" name="__codelineno-128-9" href="#__codelineno-128-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-128-10" name="__codelineno-128-10" href="#__codelineno-128-10"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span>
<a id="__codelineno-128-11" name="__codelineno-128-11" href="#__codelineno-128-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-128-12" name="__codelineno-128-12" href="#__codelineno-128-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-128-13" name="__codelineno-128-13" href="#__codelineno-128-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-128-14" name="__codelineno-128-14" href="#__codelineno-128-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-129-1" name="__codelineno-129-1" href="#__codelineno-129-1"></a><span class="cm">=begin</span>
<a id="__codelineno-129-2" name="__codelineno-129-2" href="#__codelineno-129-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-129-3" name="__codelineno-129-3" href="#__codelineno-129-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-129-4" name="__codelineno-129-4" href="#__codelineno-129-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-129-5" name="__codelineno-129-5" href="#__codelineno-129-5"></a><span class="cm">=end</span>
<a id="__codelineno-129-6" name="__codelineno-129-6" href="#__codelineno-129-6"></a>
<a id="__codelineno-129-7" name="__codelineno-129-7" href="#__codelineno-129-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-129-8" name="__codelineno-129-8" href="#__codelineno-129-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-129-9" name="__codelineno-129-9" href="#__codelineno-129-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-129-10" name="__codelineno-129-10" href="#__codelineno-129-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-129-11" name="__codelineno-129-11" href="#__codelineno-129-11"></a>
<a id="__codelineno-129-12" name="__codelineno-129-12" href="#__codelineno-129-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-129-13" name="__codelineno-129-13" href="#__codelineno-129-13"></a>
<a id="__codelineno-129-14" name="__codelineno-129-14" href="#__codelineno-129-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-129-15" name="__codelineno-129-15" href="#__codelineno-129-15"></a><span class="k">end</span>
<a id="__codelineno-129-16" name="__codelineno-129-16" href="#__codelineno-129-16"></a>
<a id="__codelineno-129-17" name="__codelineno-129-17" href="#__codelineno-129-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-129-18" name="__codelineno-129-18" href="#__codelineno-129-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-129-19" name="__codelineno-129-19" href="#__codelineno-129-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-129-20" name="__codelineno-129-20" href="#__codelineno-129-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-129-21" name="__codelineno-129-21" href="#__codelineno-129-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-129-22" name="__codelineno-129-22" href="#__codelineno-129-22"></a><span class="k">end</span>
<a id="__codelineno-129-23" name="__codelineno-129-23" href="#__codelineno-129-23"></a>
<a id="__codelineno-129-24" name="__codelineno-129-24" href="#__codelineno-129-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-129-25" name="__codelineno-129-25" href="#__codelineno-129-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-129-26" name="__codelineno-129-26" href="#__codelineno-129-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-129-27" name="__codelineno-129-27" href="#__codelineno-129-27"></a>
<a id="__codelineno-129-28" name="__codelineno-129-28" href="#__codelineno-129-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-129-29" name="__codelineno-129-29" href="#__codelineno-129-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-129-30" name="__codelineno-129-30" href="#__codelineno-129-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-129-31" name="__codelineno-129-31" href="#__codelineno-129-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-32" name="__codelineno-129-32" href="#__codelineno-129-32"></a>
<a id="__codelineno-129-33" name="__codelineno-129-33" href="#__codelineno-129-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-129-34" name="__codelineno-129-34" href="#__codelineno-129-34"></a><span class="k">end</span>
<a id="__codelineno-129-35" name="__codelineno-129-35" href="#__codelineno-129-35"></a>
<a id="__codelineno-129-36" name="__codelineno-129-36" href="#__codelineno-129-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-129-37" name="__codelineno-129-37" href="#__codelineno-129-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-129-38" name="__codelineno-129-38" href="#__codelineno-129-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-129-39" name="__codelineno-129-39" href="#__codelineno-129-39"></a>
<a id="__codelineno-129-40" name="__codelineno-129-40" href="#__codelineno-129-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-129-41" name="__codelineno-129-41" href="#__codelineno-129-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-129-42" name="__codelineno-129-42" href="#__codelineno-129-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-129-43" name="__codelineno-129-43" href="#__codelineno-129-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-129-44" name="__codelineno-129-44" href="#__codelineno-129-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-45" name="__codelineno-129-45" href="#__codelineno-129-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-46" name="__codelineno-129-46" href="#__codelineno-129-46"></a>
<a id="__codelineno-129-47" name="__codelineno-129-47" href="#__codelineno-129-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-129-48" name="__codelineno-129-48" href="#__codelineno-129-48"></a><span class="k">end</span>
<a id="__codelineno-129-49" name="__codelineno-129-49" href="#__codelineno-129-49"></a>
<a id="__codelineno-129-50" name="__codelineno-129-50" href="#__codelineno-129-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-129-51" name="__codelineno-129-51" href="#__codelineno-129-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-129-52" name="__codelineno-129-52" href="#__codelineno-129-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-129-53" name="__codelineno-129-53" href="#__codelineno-129-53"></a>
<a id="__codelineno-129-54" name="__codelineno-129-54" href="#__codelineno-129-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-129-55" name="__codelineno-129-55" href="#__codelineno-129-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-129-56" name="__codelineno-129-56" href="#__codelineno-129-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-129-57" name="__codelineno-129-57" href="#__codelineno-129-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-129-58" name="__codelineno-129-58" href="#__codelineno-129-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-129-59" name="__codelineno-129-59" href="#__codelineno-129-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-129-60" name="__codelineno-129-60" href="#__codelineno-129-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-129-61" name="__codelineno-129-61" href="#__codelineno-129-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-129-62" name="__codelineno-129-62" href="#__codelineno-129-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-129-63" name="__codelineno-129-63" href="#__codelineno-129-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-129-64" name="__codelineno-129-64" href="#__codelineno-129-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-65" name="__codelineno-129-65" href="#__codelineno-129-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-66" name="__codelineno-129-66" href="#__codelineno-129-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-67" name="__codelineno-129-67" href="#__codelineno-129-67"></a>
<a id="__codelineno-129-68" name="__codelineno-129-68" href="#__codelineno-129-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-129-69" name="__codelineno-129-69" href="#__codelineno-129-69"></a><span class="k">end</span>
<a id="__codelineno-129-70" name="__codelineno-129-70" href="#__codelineno-129-70"></a>
<a id="__codelineno-129-71" name="__codelineno-129-71" href="#__codelineno-129-71"></a><span class="c1"># ## Экспоненциальная сложность (итеративная реализация) ###</span>
<a id="__codelineno-129-72" name="__codelineno-129-72" href="#__codelineno-129-72"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-129-73" name="__codelineno-129-73" href="#__codelineno-129-73"></a><span class="w"> </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-129-74" name="__codelineno-129-74" href="#__codelineno-129-74"></a>
<a id="__codelineno-129-75" name="__codelineno-129-75" href="#__codelineno-129-75"></a><span class="w"> </span><span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-129-76" name="__codelineno-129-76" href="#__codelineno-129-76"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-129-77" name="__codelineno-129-77" href="#__codelineno-129-77"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-129-78" name="__codelineno-129-78" href="#__codelineno-129-78"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-129-79" name="__codelineno-129-79" href="#__codelineno-129-79"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-129-80" name="__codelineno-129-80" href="#__codelineno-129-80"></a>
<a id="__codelineno-129-81" name="__codelineno-129-81" href="#__codelineno-129-81"></a><span class="w"> </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-129-82" name="__codelineno-129-82" href="#__codelineno-129-82"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-129-83" name="__codelineno-129-83" href="#__codelineno-129-83"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 531px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20exponential%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20base%20%3D%201%0A%20%20%20%20%23%20%D0%9D%D0%B0%20%D0%BA%D0%B0%D0%B6%D0%B4%D0%BE%D0%BC%20%D1%88%D0%B0%D0%B3%D0%B5%20%D0%BA%D0%BB%D0%B5%D1%82%D0%BA%D0%B0%20%D0%B4%D0%B5%D0%BB%D0%B8%D1%82%D1%81%D1%8F%20%D0%BD%D0%B0%D0%B4%D0%B2%D0%BE%D0%B5%2C%20%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D1%83%D1%8F%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C%201%2C%202%2C%204%2C%208%2C%20...%2C%202%5E%28n-1%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20_%20in%20range%28base%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%20%20%20%20base%20%2A%3D%202%0A%20%20%20%20%23%20count%20%3D%201%20%2B%202%20%2B%204%20%2B%208%20%2B%20..%20%2B%202%5E%28n-1%29%20%3D%202%5En%20-%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exponential%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%8D%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20exponential%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20base%20%3D%201%0A%20%20%20%20%23%20%D0%9D%D0%B0%20%D0%BA%D0%B0%D0%B6%D0%B4%D0%BE%D0%BC%20%D1%88%D0%B0%D0%B3%D0%B5%20%D0%BA%D0%BB%D0%B5%D1%82%D0%BA%D0%B0%20%D0%B4%D0%B5%D0%BB%D0%B8%D1%82%D1%81%D1%8F%20%D0%BD%D0%B0%D0%B4%D0%B2%D0%BE%D0%B5%2C%20%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D1%83%D1%8F%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C%201%2C%202%2C%204%2C%208%2C%20...%2C%202%5E%28n-1%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20_%20in%20range%28base%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%20%20%20%20base%20%2A%3D%202%0A%20%20%20%20%23%20count%20%3D%201%20%2B%202%20%2B%204%20%2B%208%20%2B%20..%20%2B%202%5E%28n-1%29%20%3D%202%5En%20-%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exponential%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%8D%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_exponential.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Экспоненциальная временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_exponential.png" /></a></p>
<p align="center"> Рисунок 2-11 &nbsp; Экспоненциальная временная сложность </p>
<p>В реальных алгоритмах экспоненциальная сложность также часто встречается в рекурсивных функциях. Например, в следующем коде процесс рекурсивно делится надвое и останавливается после <span class="arithmatex">\(n\)</span> разбиений:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="11:13"><input checked="checked" id="__tabbed_11_1" name="__tabbed_11" type="radio" /><input id="__tabbed_11_2" name="__tabbed_11" type="radio" /><input id="__tabbed_11_3" name="__tabbed_11" type="radio" /><input id="__tabbed_11_4" name="__tabbed_11" type="radio" /><input id="__tabbed_11_5" name="__tabbed_11" type="radio" /><input id="__tabbed_11_6" name="__tabbed_11" type="radio" /><input id="__tabbed_11_7" name="__tabbed_11" type="radio" /><input id="__tabbed_11_8" name="__tabbed_11" type="radio" /><input id="__tabbed_11_9" name="__tabbed_11" type="radio" /><input id="__tabbed_11_10" name="__tabbed_11" type="radio" /><input id="__tabbed_11_11" name="__tabbed_11" type="radio" /><input id="__tabbed_11_12" name="__tabbed_11" type="radio" /><input id="__tabbed_11_13" name="__tabbed_11" type="radio" /><div class="tabbed-labels"><label for="__tabbed_11_1">Python</label><label for="__tabbed_11_2">C++</label><label for="__tabbed_11_3">Java</label><label for="__tabbed_11_4">C#</label><label for="__tabbed_11_5">Go</label><label for="__tabbed_11_6">Swift</label><label for="__tabbed_11_7">JS</label><label for="__tabbed_11_8">TS</label><label for="__tabbed_11_9">Dart</label><label for="__tabbed_11_10">Rust</label><label for="__tabbed_11_11">C</label><label for="__tabbed_11_12">Kotlin</label><label for="__tabbed_11_13">Ruby</label></div>
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<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-130-1" name="__codelineno-130-1" href="#__codelineno-130-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-130-2" name="__codelineno-130-2" href="#__codelineno-130-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Экспоненциальная сложность (рекурсивная реализация)&quot;&quot;&quot;</span>
<a id="__codelineno-130-3" name="__codelineno-130-3" href="#__codelineno-130-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<a id="__codelineno-130-4" name="__codelineno-130-4" href="#__codelineno-130-4"></a> <span class="k">return</span> <span class="mi">1</span>
<a id="__codelineno-130-5" name="__codelineno-130-5" href="#__codelineno-130-5"></a> <span class="k">return</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-131-1" name="__codelineno-131-1" href="#__codelineno-131-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-131-2" name="__codelineno-131-2" href="#__codelineno-131-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-131-3" name="__codelineno-131-3" href="#__codelineno-131-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-131-4" name="__codelineno-131-4" href="#__codelineno-131-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-131-5" name="__codelineno-131-5" href="#__codelineno-131-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-131-6" name="__codelineno-131-6" href="#__codelineno-131-6"></a><span class="p">}</span>
</code></pre></div>
</div>
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<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-132-2" name="__codelineno-132-2" href="#__codelineno-132-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-132-3" name="__codelineno-132-3" href="#__codelineno-132-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-132-4" name="__codelineno-132-4" href="#__codelineno-132-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-132-5" name="__codelineno-132-5" href="#__codelineno-132-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-132-6" name="__codelineno-132-6" href="#__codelineno-132-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-133-2" name="__codelineno-133-2" href="#__codelineno-133-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ExpRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-133-3" name="__codelineno-133-3" href="#__codelineno-133-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-133-4" name="__codelineno-133-4" href="#__codelineno-133-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">ExpRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">ExpRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-133-5" name="__codelineno-133-5" href="#__codelineno-133-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-134-1" name="__codelineno-134-1" href="#__codelineno-134-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-134-2" name="__codelineno-134-2" href="#__codelineno-134-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-134-3" name="__codelineno-134-3" href="#__codelineno-134-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-134-4" name="__codelineno-134-4" href="#__codelineno-134-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-134-5" name="__codelineno-134-5" href="#__codelineno-134-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-134-6" name="__codelineno-134-6" href="#__codelineno-134-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-134-7" name="__codelineno-134-7" href="#__codelineno-134-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-135-1" name="__codelineno-135-1" href="#__codelineno-135-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-135-2" name="__codelineno-135-2" href="#__codelineno-135-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-135-3" name="__codelineno-135-3" href="#__codelineno-135-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-135-4" name="__codelineno-135-4" href="#__codelineno-135-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-135-5" name="__codelineno-135-5" href="#__codelineno-135-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-135-6" name="__codelineno-135-6" href="#__codelineno-135-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-135-7" name="__codelineno-135-7" href="#__codelineno-135-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-136-1" name="__codelineno-136-1" href="#__codelineno-136-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-136-2" name="__codelineno-136-2" href="#__codelineno-136-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-136-3" name="__codelineno-136-3" href="#__codelineno-136-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-136-4" name="__codelineno-136-4" href="#__codelineno-136-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-136-5" name="__codelineno-136-5" href="#__codelineno-136-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-137-1" name="__codelineno-137-1" href="#__codelineno-137-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-137-2" name="__codelineno-137-2" href="#__codelineno-137-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-137-3" name="__codelineno-137-3" href="#__codelineno-137-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-137-4" name="__codelineno-137-4" href="#__codelineno-137-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-137-5" name="__codelineno-137-5" href="#__codelineno-137-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-138-1" name="__codelineno-138-1" href="#__codelineno-138-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-138-2" name="__codelineno-138-2" href="#__codelineno-138-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-138-3" name="__codelineno-138-3" href="#__codelineno-138-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-138-4" name="__codelineno-138-4" href="#__codelineno-138-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-138-5" name="__codelineno-138-5" href="#__codelineno-138-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-139-1" name="__codelineno-139-1" href="#__codelineno-139-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-139-2" name="__codelineno-139-2" href="#__codelineno-139-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-139-3" name="__codelineno-139-3" href="#__codelineno-139-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-139-4" name="__codelineno-139-4" href="#__codelineno-139-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-139-5" name="__codelineno-139-5" href="#__codelineno-139-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-139-6" name="__codelineno-139-6" href="#__codelineno-139-6"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-139-7" name="__codelineno-139-7" href="#__codelineno-139-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-140-1" name="__codelineno-140-1" href="#__codelineno-140-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-140-2" name="__codelineno-140-2" href="#__codelineno-140-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-140-3" name="__codelineno-140-3" href="#__codelineno-140-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-140-4" name="__codelineno-140-4" href="#__codelineno-140-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-140-5" name="__codelineno-140-5" href="#__codelineno-140-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-140-6" name="__codelineno-140-6" href="#__codelineno-140-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-141-1" name="__codelineno-141-1" href="#__codelineno-141-1"></a><span class="cm">/* Экспоненциальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-141-2" name="__codelineno-141-2" href="#__codelineno-141-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-141-3" name="__codelineno-141-3" href="#__codelineno-141-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-141-4" name="__codelineno-141-4" href="#__codelineno-141-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-141-5" name="__codelineno-141-5" href="#__codelineno-141-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-141-6" name="__codelineno-141-6" href="#__codelineno-141-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-141-7" name="__codelineno-141-7" href="#__codelineno-141-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="cm">=begin</span>
<a id="__codelineno-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-142-3" name="__codelineno-142-3" href="#__codelineno-142-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-142-4" name="__codelineno-142-4" href="#__codelineno-142-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-142-5" name="__codelineno-142-5" href="#__codelineno-142-5"></a><span class="cm">=end</span>
<a id="__codelineno-142-6" name="__codelineno-142-6" href="#__codelineno-142-6"></a>
<a id="__codelineno-142-7" name="__codelineno-142-7" href="#__codelineno-142-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-142-8" name="__codelineno-142-8" href="#__codelineno-142-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-142-9" name="__codelineno-142-9" href="#__codelineno-142-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-142-10" name="__codelineno-142-10" href="#__codelineno-142-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-142-11" name="__codelineno-142-11" href="#__codelineno-142-11"></a>
<a id="__codelineno-142-12" name="__codelineno-142-12" href="#__codelineno-142-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-142-13" name="__codelineno-142-13" href="#__codelineno-142-13"></a>
<a id="__codelineno-142-14" name="__codelineno-142-14" href="#__codelineno-142-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-142-15" name="__codelineno-142-15" href="#__codelineno-142-15"></a><span class="k">end</span>
<a id="__codelineno-142-16" name="__codelineno-142-16" href="#__codelineno-142-16"></a>
<a id="__codelineno-142-17" name="__codelineno-142-17" href="#__codelineno-142-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-142-18" name="__codelineno-142-18" href="#__codelineno-142-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-142-19" name="__codelineno-142-19" href="#__codelineno-142-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-142-20" name="__codelineno-142-20" href="#__codelineno-142-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-142-21" name="__codelineno-142-21" href="#__codelineno-142-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-142-22" name="__codelineno-142-22" href="#__codelineno-142-22"></a><span class="k">end</span>
<a id="__codelineno-142-23" name="__codelineno-142-23" href="#__codelineno-142-23"></a>
<a id="__codelineno-142-24" name="__codelineno-142-24" href="#__codelineno-142-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-142-25" name="__codelineno-142-25" href="#__codelineno-142-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-142-26" name="__codelineno-142-26" href="#__codelineno-142-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-142-27" name="__codelineno-142-27" href="#__codelineno-142-27"></a>
<a id="__codelineno-142-28" name="__codelineno-142-28" href="#__codelineno-142-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-142-29" name="__codelineno-142-29" href="#__codelineno-142-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-142-30" name="__codelineno-142-30" href="#__codelineno-142-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-142-31" name="__codelineno-142-31" href="#__codelineno-142-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-32" name="__codelineno-142-32" href="#__codelineno-142-32"></a>
<a id="__codelineno-142-33" name="__codelineno-142-33" href="#__codelineno-142-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-142-34" name="__codelineno-142-34" href="#__codelineno-142-34"></a><span class="k">end</span>
<a id="__codelineno-142-35" name="__codelineno-142-35" href="#__codelineno-142-35"></a>
<a id="__codelineno-142-36" name="__codelineno-142-36" href="#__codelineno-142-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-142-37" name="__codelineno-142-37" href="#__codelineno-142-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-142-38" name="__codelineno-142-38" href="#__codelineno-142-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-142-39" name="__codelineno-142-39" href="#__codelineno-142-39"></a>
<a id="__codelineno-142-40" name="__codelineno-142-40" href="#__codelineno-142-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-142-41" name="__codelineno-142-41" href="#__codelineno-142-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-142-42" name="__codelineno-142-42" href="#__codelineno-142-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-142-43" name="__codelineno-142-43" href="#__codelineno-142-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-142-44" name="__codelineno-142-44" href="#__codelineno-142-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-45" name="__codelineno-142-45" href="#__codelineno-142-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-46" name="__codelineno-142-46" href="#__codelineno-142-46"></a>
<a id="__codelineno-142-47" name="__codelineno-142-47" href="#__codelineno-142-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-142-48" name="__codelineno-142-48" href="#__codelineno-142-48"></a><span class="k">end</span>
<a id="__codelineno-142-49" name="__codelineno-142-49" href="#__codelineno-142-49"></a>
<a id="__codelineno-142-50" name="__codelineno-142-50" href="#__codelineno-142-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-142-51" name="__codelineno-142-51" href="#__codelineno-142-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-142-52" name="__codelineno-142-52" href="#__codelineno-142-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-142-53" name="__codelineno-142-53" href="#__codelineno-142-53"></a>
<a id="__codelineno-142-54" name="__codelineno-142-54" href="#__codelineno-142-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-142-55" name="__codelineno-142-55" href="#__codelineno-142-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-142-56" name="__codelineno-142-56" href="#__codelineno-142-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-142-57" name="__codelineno-142-57" href="#__codelineno-142-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-142-58" name="__codelineno-142-58" href="#__codelineno-142-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-142-59" name="__codelineno-142-59" href="#__codelineno-142-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-142-60" name="__codelineno-142-60" href="#__codelineno-142-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-142-61" name="__codelineno-142-61" href="#__codelineno-142-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-142-62" name="__codelineno-142-62" href="#__codelineno-142-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-142-63" name="__codelineno-142-63" href="#__codelineno-142-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-142-64" name="__codelineno-142-64" href="#__codelineno-142-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-65" name="__codelineno-142-65" href="#__codelineno-142-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-66" name="__codelineno-142-66" href="#__codelineno-142-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-67" name="__codelineno-142-67" href="#__codelineno-142-67"></a>
<a id="__codelineno-142-68" name="__codelineno-142-68" href="#__codelineno-142-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-142-69" name="__codelineno-142-69" href="#__codelineno-142-69"></a><span class="k">end</span>
<a id="__codelineno-142-70" name="__codelineno-142-70" href="#__codelineno-142-70"></a>
<a id="__codelineno-142-71" name="__codelineno-142-71" href="#__codelineno-142-71"></a><span class="c1"># ## Экспоненциальная сложность (итеративная реализация) ###</span>
<a id="__codelineno-142-72" name="__codelineno-142-72" href="#__codelineno-142-72"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-142-73" name="__codelineno-142-73" href="#__codelineno-142-73"></a><span class="w"> </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-142-74" name="__codelineno-142-74" href="#__codelineno-142-74"></a>
<a id="__codelineno-142-75" name="__codelineno-142-75" href="#__codelineno-142-75"></a><span class="w"> </span><span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-142-76" name="__codelineno-142-76" href="#__codelineno-142-76"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-142-77" name="__codelineno-142-77" href="#__codelineno-142-77"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-142-78" name="__codelineno-142-78" href="#__codelineno-142-78"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-142-79" name="__codelineno-142-79" href="#__codelineno-142-79"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-142-80" name="__codelineno-142-80" href="#__codelineno-142-80"></a>
<a id="__codelineno-142-81" name="__codelineno-142-81" href="#__codelineno-142-81"></a><span class="w"> </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-142-82" name="__codelineno-142-82" href="#__codelineno-142-82"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-142-83" name="__codelineno-142-83" href="#__codelineno-142-83"></a><span class="k">end</span>
<a id="__codelineno-142-84" name="__codelineno-142-84" href="#__codelineno-142-84"></a>
<a id="__codelineno-142-85" name="__codelineno-142-85" href="#__codelineno-142-85"></a><span class="c1"># ## Экспоненциальная сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-142-86" name="__codelineno-142-86" href="#__codelineno-142-86"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-142-87" name="__codelineno-142-87" href="#__codelineno-142-87"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-142-88" name="__codelineno-142-88" href="#__codelineno-142-88"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-142-89" name="__codelineno-142-89" href="#__codelineno-142-89"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20exp_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20return%20exp_recur%28n%20-%201%29%20%2B%20exp_recur%28n%20-%201%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%207%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exp_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%8D%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20exp_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20return%20exp_recur%28n%20-%201%29%20%2B%20exp_recur%28n%20-%201%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%207%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exp_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%8D%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p>Экспоненциальный рост происходит очень быстро и часто встречается в переборных методах (грубая сила, backtracking и т.д.). Для задач большого масштаба экспоненциальная сложность неприемлема, и обычно приходится применять динамическое программирование, жадные алгоритмы и другие подходы.</p>
<h3 id="5-olog-n">5. &nbsp; Логарифмическая сложность <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
<p>В противоположность экспоненциальной, логарифмическая сложность описывает ситуацию "каждый раунд уменьшение вдвое". Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> ; так как на каждом шаге размер уменьшается вдвое, число итераций равно <span class="arithmatex">\(\log_2 n\)</span> , то есть является обратной функцией к <span class="arithmatex">\(2^n\)</span> .</p>
<p>На рисунке 2-12 и в следующем коде моделируется процесс "каждый раунд уменьшение вдвое"; временная сложность равна <span class="arithmatex">\(O(\log_2 n)\)</span> и кратко записывается как <span class="arithmatex">\(O(\log n)\)</span> :</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-143-1" name="__codelineno-143-1" href="#__codelineno-143-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-143-2" name="__codelineno-143-2" href="#__codelineno-143-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Логарифмическая сложность (итеративная реализация)&quot;&quot;&quot;</span>
<a id="__codelineno-143-3" name="__codelineno-143-3" href="#__codelineno-143-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-143-4" name="__codelineno-143-4" href="#__codelineno-143-4"></a> <span class="k">while</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
<a id="__codelineno-143-5" name="__codelineno-143-5" href="#__codelineno-143-5"></a> <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
<a id="__codelineno-143-6" name="__codelineno-143-6" href="#__codelineno-143-6"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-143-7" name="__codelineno-143-7" href="#__codelineno-143-7"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-144-2" name="__codelineno-144-2" href="#__codelineno-144-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-144-3" name="__codelineno-144-3" href="#__codelineno-144-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-144-4" name="__codelineno-144-4" href="#__codelineno-144-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-144-5" name="__codelineno-144-5" href="#__codelineno-144-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-144-6" name="__codelineno-144-6" href="#__codelineno-144-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-144-7" name="__codelineno-144-7" href="#__codelineno-144-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-144-8" name="__codelineno-144-8" href="#__codelineno-144-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-144-9" name="__codelineno-144-9" href="#__codelineno-144-9"></a><span class="p">}</span>
</code></pre></div>
</div>
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<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-145-1" name="__codelineno-145-1" href="#__codelineno-145-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-145-2" name="__codelineno-145-2" href="#__codelineno-145-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-145-3" name="__codelineno-145-3" href="#__codelineno-145-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-145-4" name="__codelineno-145-4" href="#__codelineno-145-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-145-5" name="__codelineno-145-5" href="#__codelineno-145-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-145-6" name="__codelineno-145-6" href="#__codelineno-145-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-145-7" name="__codelineno-145-7" href="#__codelineno-145-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-145-8" name="__codelineno-145-8" href="#__codelineno-145-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-145-9" name="__codelineno-145-9" href="#__codelineno-145-9"></a><span class="p">}</span>
</code></pre></div>
</div>
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<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-146-1" name="__codelineno-146-1" href="#__codelineno-146-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-146-2" name="__codelineno-146-2" href="#__codelineno-146-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-146-3" name="__codelineno-146-3" href="#__codelineno-146-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-146-4" name="__codelineno-146-4" href="#__codelineno-146-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-146-5" name="__codelineno-146-5" href="#__codelineno-146-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-146-6" name="__codelineno-146-6" href="#__codelineno-146-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-146-7" name="__codelineno-146-7" href="#__codelineno-146-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-146-8" name="__codelineno-146-8" href="#__codelineno-146-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-146-9" name="__codelineno-146-9" href="#__codelineno-146-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-147-1" name="__codelineno-147-1" href="#__codelineno-147-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-147-2" name="__codelineno-147-2" href="#__codelineno-147-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-147-3" name="__codelineno-147-3" href="#__codelineno-147-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-147-4" name="__codelineno-147-4" href="#__codelineno-147-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-147-5" name="__codelineno-147-5" href="#__codelineno-147-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-147-6" name="__codelineno-147-6" href="#__codelineno-147-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-147-7" name="__codelineno-147-7" href="#__codelineno-147-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-147-8" name="__codelineno-147-8" href="#__codelineno-147-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-147-9" name="__codelineno-147-9" href="#__codelineno-147-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-148-1" name="__codelineno-148-1" href="#__codelineno-148-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-148-2" name="__codelineno-148-2" href="#__codelineno-148-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-148-3" name="__codelineno-148-3" href="#__codelineno-148-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-148-4" name="__codelineno-148-4" href="#__codelineno-148-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span>
<a id="__codelineno-148-5" name="__codelineno-148-5" href="#__codelineno-148-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-148-6" name="__codelineno-148-6" href="#__codelineno-148-6"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-148-7" name="__codelineno-148-7" href="#__codelineno-148-7"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-148-8" name="__codelineno-148-8" href="#__codelineno-148-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-148-9" name="__codelineno-148-9" href="#__codelineno-148-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-148-10" name="__codelineno-148-10" href="#__codelineno-148-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-149-1" name="__codelineno-149-1" href="#__codelineno-149-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-149-2" name="__codelineno-149-2" href="#__codelineno-149-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-149-3" name="__codelineno-149-3" href="#__codelineno-149-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-149-4" name="__codelineno-149-4" href="#__codelineno-149-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-149-5" name="__codelineno-149-5" href="#__codelineno-149-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a id="__codelineno-149-6" name="__codelineno-149-6" href="#__codelineno-149-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-149-7" name="__codelineno-149-7" href="#__codelineno-149-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-149-8" name="__codelineno-149-8" href="#__codelineno-149-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-149-9" name="__codelineno-149-9" href="#__codelineno-149-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-150-1" name="__codelineno-150-1" href="#__codelineno-150-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-150-2" name="__codelineno-150-2" href="#__codelineno-150-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-150-3" name="__codelineno-150-3" href="#__codelineno-150-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-150-4" name="__codelineno-150-4" href="#__codelineno-150-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-150-5" name="__codelineno-150-5" href="#__codelineno-150-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a id="__codelineno-150-6" name="__codelineno-150-6" href="#__codelineno-150-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-150-7" name="__codelineno-150-7" href="#__codelineno-150-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-150-8" name="__codelineno-150-8" href="#__codelineno-150-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-150-9" name="__codelineno-150-9" href="#__codelineno-150-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-151-1" name="__codelineno-151-1" href="#__codelineno-151-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-151-2" name="__codelineno-151-2" href="#__codelineno-151-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-151-3" name="__codelineno-151-3" href="#__codelineno-151-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-151-4" name="__codelineno-151-4" href="#__codelineno-151-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-151-5" name="__codelineno-151-5" href="#__codelineno-151-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
<a id="__codelineno-151-6" name="__codelineno-151-6" href="#__codelineno-151-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-151-7" name="__codelineno-151-7" href="#__codelineno-151-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-151-8" name="__codelineno-151-8" href="#__codelineno-151-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-151-9" name="__codelineno-151-9" href="#__codelineno-151-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-152-6" name="__codelineno-152-6" href="#__codelineno-152-6"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-152-7" name="__codelineno-152-7" href="#__codelineno-152-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-152-8" name="__codelineno-152-8" href="#__codelineno-152-8"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-152-9" name="__codelineno-152-9" href="#__codelineno-152-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-153-1" name="__codelineno-153-1" href="#__codelineno-153-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-153-2" name="__codelineno-153-2" href="#__codelineno-153-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-153-3" name="__codelineno-153-3" href="#__codelineno-153-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-153-4" name="__codelineno-153-4" href="#__codelineno-153-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-153-5" name="__codelineno-153-5" href="#__codelineno-153-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-153-6" name="__codelineno-153-6" href="#__codelineno-153-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-153-7" name="__codelineno-153-7" href="#__codelineno-153-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-153-8" name="__codelineno-153-8" href="#__codelineno-153-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-153-9" name="__codelineno-153-9" href="#__codelineno-153-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-154-1" name="__codelineno-154-1" href="#__codelineno-154-1"></a><span class="cm">/* Логарифмическая сложность (итеративная реализация) */</span>
<a id="__codelineno-154-2" name="__codelineno-154-2" href="#__codelineno-154-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-154-3" name="__codelineno-154-3" href="#__codelineno-154-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span>
<a id="__codelineno-154-4" name="__codelineno-154-4" href="#__codelineno-154-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-154-5" name="__codelineno-154-5" href="#__codelineno-154-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n1</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-154-6" name="__codelineno-154-6" href="#__codelineno-154-6"></a><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="m">2</span>
<a id="__codelineno-154-7" name="__codelineno-154-7" href="#__codelineno-154-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-154-8" name="__codelineno-154-8" href="#__codelineno-154-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-154-9" name="__codelineno-154-9" href="#__codelineno-154-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-154-10" name="__codelineno-154-10" href="#__codelineno-154-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-155-1" name="__codelineno-155-1" href="#__codelineno-155-1"></a><span class="cm">=begin</span>
<a id="__codelineno-155-2" name="__codelineno-155-2" href="#__codelineno-155-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-155-3" name="__codelineno-155-3" href="#__codelineno-155-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-155-4" name="__codelineno-155-4" href="#__codelineno-155-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-155-5" name="__codelineno-155-5" href="#__codelineno-155-5"></a><span class="cm">=end</span>
<a id="__codelineno-155-6" name="__codelineno-155-6" href="#__codelineno-155-6"></a>
<a id="__codelineno-155-7" name="__codelineno-155-7" href="#__codelineno-155-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-155-8" name="__codelineno-155-8" href="#__codelineno-155-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-155-9" name="__codelineno-155-9" href="#__codelineno-155-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-155-10" name="__codelineno-155-10" href="#__codelineno-155-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-155-11" name="__codelineno-155-11" href="#__codelineno-155-11"></a>
<a id="__codelineno-155-12" name="__codelineno-155-12" href="#__codelineno-155-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-155-13" name="__codelineno-155-13" href="#__codelineno-155-13"></a>
<a id="__codelineno-155-14" name="__codelineno-155-14" href="#__codelineno-155-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-15" name="__codelineno-155-15" href="#__codelineno-155-15"></a><span class="k">end</span>
<a id="__codelineno-155-16" name="__codelineno-155-16" href="#__codelineno-155-16"></a>
<a id="__codelineno-155-17" name="__codelineno-155-17" href="#__codelineno-155-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-155-18" name="__codelineno-155-18" href="#__codelineno-155-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-155-19" name="__codelineno-155-19" href="#__codelineno-155-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-155-20" name="__codelineno-155-20" href="#__codelineno-155-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-155-21" name="__codelineno-155-21" href="#__codelineno-155-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-22" name="__codelineno-155-22" href="#__codelineno-155-22"></a><span class="k">end</span>
<a id="__codelineno-155-23" name="__codelineno-155-23" href="#__codelineno-155-23"></a>
<a id="__codelineno-155-24" name="__codelineno-155-24" href="#__codelineno-155-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-155-25" name="__codelineno-155-25" href="#__codelineno-155-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-155-26" name="__codelineno-155-26" href="#__codelineno-155-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-155-27" name="__codelineno-155-27" href="#__codelineno-155-27"></a>
<a id="__codelineno-155-28" name="__codelineno-155-28" href="#__codelineno-155-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-155-29" name="__codelineno-155-29" href="#__codelineno-155-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-155-30" name="__codelineno-155-30" href="#__codelineno-155-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-31" name="__codelineno-155-31" href="#__codelineno-155-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-32" name="__codelineno-155-32" href="#__codelineno-155-32"></a>
<a id="__codelineno-155-33" name="__codelineno-155-33" href="#__codelineno-155-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-34" name="__codelineno-155-34" href="#__codelineno-155-34"></a><span class="k">end</span>
<a id="__codelineno-155-35" name="__codelineno-155-35" href="#__codelineno-155-35"></a>
<a id="__codelineno-155-36" name="__codelineno-155-36" href="#__codelineno-155-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-155-37" name="__codelineno-155-37" href="#__codelineno-155-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-155-38" name="__codelineno-155-38" href="#__codelineno-155-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-155-39" name="__codelineno-155-39" href="#__codelineno-155-39"></a>
<a id="__codelineno-155-40" name="__codelineno-155-40" href="#__codelineno-155-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-155-41" name="__codelineno-155-41" href="#__codelineno-155-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-155-42" name="__codelineno-155-42" href="#__codelineno-155-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-155-43" name="__codelineno-155-43" href="#__codelineno-155-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-44" name="__codelineno-155-44" href="#__codelineno-155-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-45" name="__codelineno-155-45" href="#__codelineno-155-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-46" name="__codelineno-155-46" href="#__codelineno-155-46"></a>
<a id="__codelineno-155-47" name="__codelineno-155-47" href="#__codelineno-155-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-48" name="__codelineno-155-48" href="#__codelineno-155-48"></a><span class="k">end</span>
<a id="__codelineno-155-49" name="__codelineno-155-49" href="#__codelineno-155-49"></a>
<a id="__codelineno-155-50" name="__codelineno-155-50" href="#__codelineno-155-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-155-51" name="__codelineno-155-51" href="#__codelineno-155-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-155-52" name="__codelineno-155-52" href="#__codelineno-155-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-155-53" name="__codelineno-155-53" href="#__codelineno-155-53"></a>
<a id="__codelineno-155-54" name="__codelineno-155-54" href="#__codelineno-155-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-155-55" name="__codelineno-155-55" href="#__codelineno-155-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-155-56" name="__codelineno-155-56" href="#__codelineno-155-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-155-57" name="__codelineno-155-57" href="#__codelineno-155-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-155-58" name="__codelineno-155-58" href="#__codelineno-155-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-155-59" name="__codelineno-155-59" href="#__codelineno-155-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-155-60" name="__codelineno-155-60" href="#__codelineno-155-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-155-61" name="__codelineno-155-61" href="#__codelineno-155-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-155-62" name="__codelineno-155-62" href="#__codelineno-155-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-155-63" name="__codelineno-155-63" href="#__codelineno-155-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-155-64" name="__codelineno-155-64" href="#__codelineno-155-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-65" name="__codelineno-155-65" href="#__codelineno-155-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-66" name="__codelineno-155-66" href="#__codelineno-155-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-67" name="__codelineno-155-67" href="#__codelineno-155-67"></a>
<a id="__codelineno-155-68" name="__codelineno-155-68" href="#__codelineno-155-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-69" name="__codelineno-155-69" href="#__codelineno-155-69"></a><span class="k">end</span>
<a id="__codelineno-155-70" name="__codelineno-155-70" href="#__codelineno-155-70"></a>
<a id="__codelineno-155-71" name="__codelineno-155-71" href="#__codelineno-155-71"></a><span class="c1"># ## Экспоненциальная сложность (итеративная реализация) ###</span>
<a id="__codelineno-155-72" name="__codelineno-155-72" href="#__codelineno-155-72"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-155-73" name="__codelineno-155-73" href="#__codelineno-155-73"></a><span class="w"> </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-74" name="__codelineno-155-74" href="#__codelineno-155-74"></a>
<a id="__codelineno-155-75" name="__codelineno-155-75" href="#__codelineno-155-75"></a><span class="w"> </span><span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-155-76" name="__codelineno-155-76" href="#__codelineno-155-76"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-155-77" name="__codelineno-155-77" href="#__codelineno-155-77"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-155-78" name="__codelineno-155-78" href="#__codelineno-155-78"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-155-79" name="__codelineno-155-79" href="#__codelineno-155-79"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-80" name="__codelineno-155-80" href="#__codelineno-155-80"></a>
<a id="__codelineno-155-81" name="__codelineno-155-81" href="#__codelineno-155-81"></a><span class="w"> </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-155-82" name="__codelineno-155-82" href="#__codelineno-155-82"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-83" name="__codelineno-155-83" href="#__codelineno-155-83"></a><span class="k">end</span>
<a id="__codelineno-155-84" name="__codelineno-155-84" href="#__codelineno-155-84"></a>
<a id="__codelineno-155-85" name="__codelineno-155-85" href="#__codelineno-155-85"></a><span class="c1"># ## Экспоненциальная сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-155-86" name="__codelineno-155-86" href="#__codelineno-155-86"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-155-87" name="__codelineno-155-87" href="#__codelineno-155-87"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-88" name="__codelineno-155-88" href="#__codelineno-155-88"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-89" name="__codelineno-155-89" href="#__codelineno-155-89"></a><span class="k">end</span>
<a id="__codelineno-155-90" name="__codelineno-155-90" href="#__codelineno-155-90"></a>
<a id="__codelineno-155-91" name="__codelineno-155-91" href="#__codelineno-155-91"></a><span class="c1"># ## Логарифмическая сложность (итеративная реализация) ###</span>
<a id="__codelineno-155-92" name="__codelineno-155-92" href="#__codelineno-155-92"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-155-93" name="__codelineno-155-93" href="#__codelineno-155-93"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-155-94" name="__codelineno-155-94" href="#__codelineno-155-94"></a>
<a id="__codelineno-155-95" name="__codelineno-155-95" href="#__codelineno-155-95"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-96" name="__codelineno-155-96" href="#__codelineno-155-96"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-155-97" name="__codelineno-155-97" href="#__codelineno-155-97"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-155-98" name="__codelineno-155-98" href="#__codelineno-155-98"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-155-99" name="__codelineno-155-99" href="#__codelineno-155-99"></a>
<a id="__codelineno-155-100" name="__codelineno-155-100" href="#__codelineno-155-100"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-155-101" name="__codelineno-155-101" href="#__codelineno-155-101"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20%2F%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20%2F%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_logarithmic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Логарифмическая временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic.png" /></a></p>
<p align="center"> Рисунок 2-12 &nbsp; Логарифмическая временная сложность </p>
<p>Подобно экспоненциальной сложности, логарифмическая также часто встречается в рекурсивных функциях. Следующий код формирует рекурсивное дерево высотой <span class="arithmatex">\(\log_2 n\)</span> :</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-156-2" name="__codelineno-156-2" href="#__codelineno-156-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Логарифмическая сложность (рекурсивная реализация)&quot;&quot;&quot;</span>
<a id="__codelineno-156-3" name="__codelineno-156-3" href="#__codelineno-156-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
<a id="__codelineno-156-4" name="__codelineno-156-4" href="#__codelineno-156-4"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-156-5" name="__codelineno-156-5" href="#__codelineno-156-5"></a> <span class="k">return</span> <span class="n">log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-157-1" name="__codelineno-157-1" href="#__codelineno-157-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-157-2" name="__codelineno-157-2" href="#__codelineno-157-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-157-3" name="__codelineno-157-3" href="#__codelineno-157-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-157-4" name="__codelineno-157-4" href="#__codelineno-157-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-157-5" name="__codelineno-157-5" href="#__codelineno-157-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-157-6" name="__codelineno-157-6" href="#__codelineno-157-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-158-1" name="__codelineno-158-1" href="#__codelineno-158-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-158-2" name="__codelineno-158-2" href="#__codelineno-158-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-158-3" name="__codelineno-158-3" href="#__codelineno-158-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-158-4" name="__codelineno-158-4" href="#__codelineno-158-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-158-5" name="__codelineno-158-5" href="#__codelineno-158-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-158-6" name="__codelineno-158-6" href="#__codelineno-158-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-159-1" name="__codelineno-159-1" href="#__codelineno-159-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-159-2" name="__codelineno-159-2" href="#__codelineno-159-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-159-3" name="__codelineno-159-3" href="#__codelineno-159-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-159-4" name="__codelineno-159-4" href="#__codelineno-159-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">LogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-159-5" name="__codelineno-159-5" href="#__codelineno-159-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-160-1" name="__codelineno-160-1" href="#__codelineno-160-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-160-2" name="__codelineno-160-2" href="#__codelineno-160-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-160-3" name="__codelineno-160-3" href="#__codelineno-160-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-160-4" name="__codelineno-160-4" href="#__codelineno-160-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-160-5" name="__codelineno-160-5" href="#__codelineno-160-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-160-6" name="__codelineno-160-6" href="#__codelineno-160-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-161-1" name="__codelineno-161-1" href="#__codelineno-161-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-161-2" name="__codelineno-161-2" href="#__codelineno-161-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-161-3" name="__codelineno-161-3" href="#__codelineno-161-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-161-4" name="__codelineno-161-4" href="#__codelineno-161-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-161-5" name="__codelineno-161-5" href="#__codelineno-161-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-161-6" name="__codelineno-161-6" href="#__codelineno-161-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-161-7" name="__codelineno-161-7" href="#__codelineno-161-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-162-1" name="__codelineno-162-1" href="#__codelineno-162-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-162-2" name="__codelineno-162-2" href="#__codelineno-162-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-162-3" name="__codelineno-162-3" href="#__codelineno-162-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-162-4" name="__codelineno-162-4" href="#__codelineno-162-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-162-5" name="__codelineno-162-5" href="#__codelineno-162-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-163-1" name="__codelineno-163-1" href="#__codelineno-163-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-163-2" name="__codelineno-163-2" href="#__codelineno-163-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-163-3" name="__codelineno-163-3" href="#__codelineno-163-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-163-4" name="__codelineno-163-4" href="#__codelineno-163-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-163-5" name="__codelineno-163-5" href="#__codelineno-163-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-164-1" name="__codelineno-164-1" href="#__codelineno-164-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-164-2" name="__codelineno-164-2" href="#__codelineno-164-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-164-3" name="__codelineno-164-3" href="#__codelineno-164-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-164-4" name="__codelineno-164-4" href="#__codelineno-164-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-164-5" name="__codelineno-164-5" href="#__codelineno-164-5"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-165-1" name="__codelineno-165-1" href="#__codelineno-165-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-165-4" name="__codelineno-165-4" href="#__codelineno-165-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a><span class="w"> </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-166-1" name="__codelineno-166-1" href="#__codelineno-166-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-166-3" name="__codelineno-166-3" href="#__codelineno-166-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-166-4" name="__codelineno-166-4" href="#__codelineno-166-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-166-5" name="__codelineno-166-5" href="#__codelineno-166-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-166-6" name="__codelineno-166-6" href="#__codelineno-166-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="cm">/* Логарифмическая сложность (рекурсивная реализация) */</span>
<a id="__codelineno-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-167-3" name="__codelineno-167-3" href="#__codelineno-167-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
<a id="__codelineno-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-168-1" name="__codelineno-168-1" href="#__codelineno-168-1"></a><span class="cm">=begin</span>
<a id="__codelineno-168-2" name="__codelineno-168-2" href="#__codelineno-168-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-168-3" name="__codelineno-168-3" href="#__codelineno-168-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-168-4" name="__codelineno-168-4" href="#__codelineno-168-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-168-5" name="__codelineno-168-5" href="#__codelineno-168-5"></a><span class="cm">=end</span>
<a id="__codelineno-168-6" name="__codelineno-168-6" href="#__codelineno-168-6"></a>
<a id="__codelineno-168-7" name="__codelineno-168-7" href="#__codelineno-168-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-168-8" name="__codelineno-168-8" href="#__codelineno-168-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-9" name="__codelineno-168-9" href="#__codelineno-168-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-168-10" name="__codelineno-168-10" href="#__codelineno-168-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-168-11" name="__codelineno-168-11" href="#__codelineno-168-11"></a>
<a id="__codelineno-168-12" name="__codelineno-168-12" href="#__codelineno-168-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-168-13" name="__codelineno-168-13" href="#__codelineno-168-13"></a>
<a id="__codelineno-168-14" name="__codelineno-168-14" href="#__codelineno-168-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-15" name="__codelineno-168-15" href="#__codelineno-168-15"></a><span class="k">end</span>
<a id="__codelineno-168-16" name="__codelineno-168-16" href="#__codelineno-168-16"></a>
<a id="__codelineno-168-17" name="__codelineno-168-17" href="#__codelineno-168-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-168-18" name="__codelineno-168-18" href="#__codelineno-168-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-19" name="__codelineno-168-19" href="#__codelineno-168-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-168-20" name="__codelineno-168-20" href="#__codelineno-168-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-168-21" name="__codelineno-168-21" href="#__codelineno-168-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-22" name="__codelineno-168-22" href="#__codelineno-168-22"></a><span class="k">end</span>
<a id="__codelineno-168-23" name="__codelineno-168-23" href="#__codelineno-168-23"></a>
<a id="__codelineno-168-24" name="__codelineno-168-24" href="#__codelineno-168-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-168-25" name="__codelineno-168-25" href="#__codelineno-168-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-168-26" name="__codelineno-168-26" href="#__codelineno-168-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-168-27" name="__codelineno-168-27" href="#__codelineno-168-27"></a>
<a id="__codelineno-168-28" name="__codelineno-168-28" href="#__codelineno-168-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-168-29" name="__codelineno-168-29" href="#__codelineno-168-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-168-30" name="__codelineno-168-30" href="#__codelineno-168-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-31" name="__codelineno-168-31" href="#__codelineno-168-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-32" name="__codelineno-168-32" href="#__codelineno-168-32"></a>
<a id="__codelineno-168-33" name="__codelineno-168-33" href="#__codelineno-168-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-34" name="__codelineno-168-34" href="#__codelineno-168-34"></a><span class="k">end</span>
<a id="__codelineno-168-35" name="__codelineno-168-35" href="#__codelineno-168-35"></a>
<a id="__codelineno-168-36" name="__codelineno-168-36" href="#__codelineno-168-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-168-37" name="__codelineno-168-37" href="#__codelineno-168-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-38" name="__codelineno-168-38" href="#__codelineno-168-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-168-39" name="__codelineno-168-39" href="#__codelineno-168-39"></a>
<a id="__codelineno-168-40" name="__codelineno-168-40" href="#__codelineno-168-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-168-41" name="__codelineno-168-41" href="#__codelineno-168-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-168-42" name="__codelineno-168-42" href="#__codelineno-168-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-168-43" name="__codelineno-168-43" href="#__codelineno-168-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-44" name="__codelineno-168-44" href="#__codelineno-168-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-45" name="__codelineno-168-45" href="#__codelineno-168-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-46" name="__codelineno-168-46" href="#__codelineno-168-46"></a>
<a id="__codelineno-168-47" name="__codelineno-168-47" href="#__codelineno-168-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-48" name="__codelineno-168-48" href="#__codelineno-168-48"></a><span class="k">end</span>
<a id="__codelineno-168-49" name="__codelineno-168-49" href="#__codelineno-168-49"></a>
<a id="__codelineno-168-50" name="__codelineno-168-50" href="#__codelineno-168-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-168-51" name="__codelineno-168-51" href="#__codelineno-168-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-168-52" name="__codelineno-168-52" href="#__codelineno-168-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-168-53" name="__codelineno-168-53" href="#__codelineno-168-53"></a>
<a id="__codelineno-168-54" name="__codelineno-168-54" href="#__codelineno-168-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-168-55" name="__codelineno-168-55" href="#__codelineno-168-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-168-56" name="__codelineno-168-56" href="#__codelineno-168-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-168-57" name="__codelineno-168-57" href="#__codelineno-168-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-168-58" name="__codelineno-168-58" href="#__codelineno-168-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-168-59" name="__codelineno-168-59" href="#__codelineno-168-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-168-60" name="__codelineno-168-60" href="#__codelineno-168-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-168-61" name="__codelineno-168-61" href="#__codelineno-168-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-168-62" name="__codelineno-168-62" href="#__codelineno-168-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-168-63" name="__codelineno-168-63" href="#__codelineno-168-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-168-64" name="__codelineno-168-64" href="#__codelineno-168-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-65" name="__codelineno-168-65" href="#__codelineno-168-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-66" name="__codelineno-168-66" href="#__codelineno-168-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-67" name="__codelineno-168-67" href="#__codelineno-168-67"></a>
<a id="__codelineno-168-68" name="__codelineno-168-68" href="#__codelineno-168-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-69" name="__codelineno-168-69" href="#__codelineno-168-69"></a><span class="k">end</span>
<a id="__codelineno-168-70" name="__codelineno-168-70" href="#__codelineno-168-70"></a>
<a id="__codelineno-168-71" name="__codelineno-168-71" href="#__codelineno-168-71"></a><span class="c1"># ## Экспоненциальная сложность (итеративная реализация) ###</span>
<a id="__codelineno-168-72" name="__codelineno-168-72" href="#__codelineno-168-72"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-73" name="__codelineno-168-73" href="#__codelineno-168-73"></a><span class="w"> </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-74" name="__codelineno-168-74" href="#__codelineno-168-74"></a>
<a id="__codelineno-168-75" name="__codelineno-168-75" href="#__codelineno-168-75"></a><span class="w"> </span><span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-168-76" name="__codelineno-168-76" href="#__codelineno-168-76"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-168-77" name="__codelineno-168-77" href="#__codelineno-168-77"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-168-78" name="__codelineno-168-78" href="#__codelineno-168-78"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-168-79" name="__codelineno-168-79" href="#__codelineno-168-79"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-80" name="__codelineno-168-80" href="#__codelineno-168-80"></a>
<a id="__codelineno-168-81" name="__codelineno-168-81" href="#__codelineno-168-81"></a><span class="w"> </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-168-82" name="__codelineno-168-82" href="#__codelineno-168-82"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-83" name="__codelineno-168-83" href="#__codelineno-168-83"></a><span class="k">end</span>
<a id="__codelineno-168-84" name="__codelineno-168-84" href="#__codelineno-168-84"></a>
<a id="__codelineno-168-85" name="__codelineno-168-85" href="#__codelineno-168-85"></a><span class="c1"># ## Экспоненциальная сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-168-86" name="__codelineno-168-86" href="#__codelineno-168-86"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-87" name="__codelineno-168-87" href="#__codelineno-168-87"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-88" name="__codelineno-168-88" href="#__codelineno-168-88"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-89" name="__codelineno-168-89" href="#__codelineno-168-89"></a><span class="k">end</span>
<a id="__codelineno-168-90" name="__codelineno-168-90" href="#__codelineno-168-90"></a>
<a id="__codelineno-168-91" name="__codelineno-168-91" href="#__codelineno-168-91"></a><span class="c1"># ## Логарифмическая сложность (итеративная реализация) ###</span>
<a id="__codelineno-168-92" name="__codelineno-168-92" href="#__codelineno-168-92"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-93" name="__codelineno-168-93" href="#__codelineno-168-93"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-168-94" name="__codelineno-168-94" href="#__codelineno-168-94"></a>
<a id="__codelineno-168-95" name="__codelineno-168-95" href="#__codelineno-168-95"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-96" name="__codelineno-168-96" href="#__codelineno-168-96"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-168-97" name="__codelineno-168-97" href="#__codelineno-168-97"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-98" name="__codelineno-168-98" href="#__codelineno-168-98"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-168-99" name="__codelineno-168-99" href="#__codelineno-168-99"></a>
<a id="__codelineno-168-100" name="__codelineno-168-100" href="#__codelineno-168-100"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-168-101" name="__codelineno-168-101" href="#__codelineno-168-101"></a><span class="k">end</span>
<a id="__codelineno-168-102" name="__codelineno-168-102" href="#__codelineno-168-102"></a>
<a id="__codelineno-168-103" name="__codelineno-168-103" href="#__codelineno-168-103"></a><span class="c1"># ## Логарифмическая сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-168-104" name="__codelineno-168-104" href="#__codelineno-168-104"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-168-105" name="__codelineno-168-105" href="#__codelineno-168-105"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-106" name="__codelineno-168-106" href="#__codelineno-168-106"></a><span class="w"> </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-168-107" name="__codelineno-168-107" href="#__codelineno-168-107"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20%2F%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20%2F%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p>Логарифмическая сложность часто встречается в алгоритмах, основанных на стратегии "разделяй и властвуй", и отражает идеи "разделить одно на много" и "упростить сложное". Она растет медленно и является идеальной временной сложностью, уступающей только постоянной.</p>
<div class="admonition tip">
<p class="admonition-title">Каково основание у <span class="arithmatex">\(O(\log n)\)</span> ?</p>
<p>Точнее говоря, "разделение на <span class="arithmatex">\(m\)</span> частей" соответствует временной сложности <span class="arithmatex">\(O(\log_m n)\)</span> . А по формуле перехода к другому основанию логарифма мы получаем равные по сложности выражения с разными основаниями:</p>
<div class="arithmatex">\[
O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
\]</div>
<p>Иными словами, основание <span class="arithmatex">\(m\)</span> можно менять без влияния на сложность. Поэтому мы обычно опускаем основание <span class="arithmatex">\(m\)</span> и напрямую записываем логарифмическую сложность как <span class="arithmatex">\(O(\log n)\)</span> .</p>
</div>
<h3 id="6-on-log-n">6. &nbsp; Линейно-логарифмическая сложность <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">&para;</a></h3>
<p>Линейно-логарифмическая сложность часто встречается во вложенных циклах, когда временная сложность двух уровней соответственно равна <span class="arithmatex">\(O(\log n)\)</span> и <span class="arithmatex">\(O(n)\)</span> . Соответствующий код выглядит следующим образом:</p>
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<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-169-1" name="__codelineno-169-1" href="#__codelineno-169-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-169-2" name="__codelineno-169-2" href="#__codelineno-169-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Линейно-логарифмическая сложность&quot;&quot;&quot;</span>
<a id="__codelineno-169-3" name="__codelineno-169-3" href="#__codelineno-169-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
<a id="__codelineno-169-4" name="__codelineno-169-4" href="#__codelineno-169-4"></a> <span class="k">return</span> <span class="mi">1</span>
<a id="__codelineno-169-5" name="__codelineno-169-5" href="#__codelineno-169-5"></a> <span class="c1"># Разделение надвое: размер подзадачи уменьшается вдвое</span>
<a id="__codelineno-169-6" name="__codelineno-169-6" href="#__codelineno-169-6"></a> <span class="n">count</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-169-7" name="__codelineno-169-7" href="#__codelineno-169-7"></a> <span class="c1"># Текущая подзадача содержит n операций</span>
<a id="__codelineno-169-8" name="__codelineno-169-8" href="#__codelineno-169-8"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-169-9" name="__codelineno-169-9" href="#__codelineno-169-9"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-169-10" name="__codelineno-169-10" href="#__codelineno-169-10"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-170-1" name="__codelineno-170-1" href="#__codelineno-170-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-170-2" name="__codelineno-170-2" href="#__codelineno-170-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-170-3" name="__codelineno-170-3" href="#__codelineno-170-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-170-4" name="__codelineno-170-4" href="#__codelineno-170-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-170-5" name="__codelineno-170-5" href="#__codelineno-170-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-170-6" name="__codelineno-170-6" href="#__codelineno-170-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-170-7" name="__codelineno-170-7" href="#__codelineno-170-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-170-8" name="__codelineno-170-8" href="#__codelineno-170-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-170-9" name="__codelineno-170-9" href="#__codelineno-170-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-170-10" name="__codelineno-170-10" href="#__codelineno-170-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-171-1" name="__codelineno-171-1" href="#__codelineno-171-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-171-2" name="__codelineno-171-2" href="#__codelineno-171-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-171-3" name="__codelineno-171-3" href="#__codelineno-171-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-171-4" name="__codelineno-171-4" href="#__codelineno-171-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-171-5" name="__codelineno-171-5" href="#__codelineno-171-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-171-6" name="__codelineno-171-6" href="#__codelineno-171-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-171-7" name="__codelineno-171-7" href="#__codelineno-171-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-171-8" name="__codelineno-171-8" href="#__codelineno-171-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-171-9" name="__codelineno-171-9" href="#__codelineno-171-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-171-10" name="__codelineno-171-10" href="#__codelineno-171-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-172-1" name="__codelineno-172-1" href="#__codelineno-172-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-172-2" name="__codelineno-172-2" href="#__codelineno-172-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LinearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-172-3" name="__codelineno-172-3" href="#__codelineno-172-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-172-4" name="__codelineno-172-4" href="#__codelineno-172-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">LinearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-172-5" name="__codelineno-172-5" href="#__codelineno-172-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-172-6" name="__codelineno-172-6" href="#__codelineno-172-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-172-7" name="__codelineno-172-7" href="#__codelineno-172-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-172-8" name="__codelineno-172-8" href="#__codelineno-172-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-172-9" name="__codelineno-172-9" href="#__codelineno-172-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-173-1" name="__codelineno-173-1" href="#__codelineno-173-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-173-2" name="__codelineno-173-2" href="#__codelineno-173-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-173-3" name="__codelineno-173-3" href="#__codelineno-173-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-173-4" name="__codelineno-173-4" href="#__codelineno-173-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-173-5" name="__codelineno-173-5" href="#__codelineno-173-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-173-6" name="__codelineno-173-6" href="#__codelineno-173-6"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-173-7" name="__codelineno-173-7" href="#__codelineno-173-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-173-8" name="__codelineno-173-8" href="#__codelineno-173-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-173-9" name="__codelineno-173-9" href="#__codelineno-173-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-173-10" name="__codelineno-173-10" href="#__codelineno-173-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-173-11" name="__codelineno-173-11" href="#__codelineno-173-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-174-1" name="__codelineno-174-1" href="#__codelineno-174-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-174-2" name="__codelineno-174-2" href="#__codelineno-174-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-174-3" name="__codelineno-174-3" href="#__codelineno-174-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-174-4" name="__codelineno-174-4" href="#__codelineno-174-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-174-5" name="__codelineno-174-5" href="#__codelineno-174-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-174-6" name="__codelineno-174-6" href="#__codelineno-174-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-174-7" name="__codelineno-174-7" href="#__codelineno-174-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">by</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-174-8" name="__codelineno-174-8" href="#__codelineno-174-8"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-174-9" name="__codelineno-174-9" href="#__codelineno-174-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-174-10" name="__codelineno-174-10" href="#__codelineno-174-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-174-11" name="__codelineno-174-11" href="#__codelineno-174-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-175-1" name="__codelineno-175-1" href="#__codelineno-175-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-175-2" name="__codelineno-175-2" href="#__codelineno-175-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-175-3" name="__codelineno-175-3" href="#__codelineno-175-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-175-4" name="__codelineno-175-4" href="#__codelineno-175-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
<a id="__codelineno-175-5" name="__codelineno-175-5" href="#__codelineno-175-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-175-6" name="__codelineno-175-6" href="#__codelineno-175-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-175-7" name="__codelineno-175-7" href="#__codelineno-175-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-175-8" name="__codelineno-175-8" href="#__codelineno-175-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-175-9" name="__codelineno-175-9" href="#__codelineno-175-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-176-1" name="__codelineno-176-1" href="#__codelineno-176-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-176-2" name="__codelineno-176-2" href="#__codelineno-176-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-176-3" name="__codelineno-176-3" href="#__codelineno-176-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-176-4" name="__codelineno-176-4" href="#__codelineno-176-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
<a id="__codelineno-176-5" name="__codelineno-176-5" href="#__codelineno-176-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-176-6" name="__codelineno-176-6" href="#__codelineno-176-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-176-7" name="__codelineno-176-7" href="#__codelineno-176-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-176-8" name="__codelineno-176-8" href="#__codelineno-176-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-176-9" name="__codelineno-176-9" href="#__codelineno-176-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-177-1" name="__codelineno-177-1" href="#__codelineno-177-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-177-2" name="__codelineno-177-2" href="#__codelineno-177-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-177-3" name="__codelineno-177-3" href="#__codelineno-177-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-177-4" name="__codelineno-177-4" href="#__codelineno-177-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
<a id="__codelineno-177-5" name="__codelineno-177-5" href="#__codelineno-177-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-177-6" name="__codelineno-177-6" href="#__codelineno-177-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-177-7" name="__codelineno-177-7" href="#__codelineno-177-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-177-8" name="__codelineno-177-8" href="#__codelineno-177-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-177-9" name="__codelineno-177-9" href="#__codelineno-177-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-178-1" name="__codelineno-178-1" href="#__codelineno-178-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-178-2" name="__codelineno-178-2" href="#__codelineno-178-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-178-3" name="__codelineno-178-3" href="#__codelineno-178-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-178-4" name="__codelineno-178-4" href="#__codelineno-178-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-178-5" name="__codelineno-178-5" href="#__codelineno-178-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-178-6" name="__codelineno-178-6" href="#__codelineno-178-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-178-7" name="__codelineno-178-7" href="#__codelineno-178-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-178-8" name="__codelineno-178-8" href="#__codelineno-178-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-178-9" name="__codelineno-178-9" href="#__codelineno-178-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-178-10" name="__codelineno-178-10" href="#__codelineno-178-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-178-11" name="__codelineno-178-11" href="#__codelineno-178-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-179-1" name="__codelineno-179-1" href="#__codelineno-179-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-179-2" name="__codelineno-179-2" href="#__codelineno-179-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-179-3" name="__codelineno-179-3" href="#__codelineno-179-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-179-4" name="__codelineno-179-4" href="#__codelineno-179-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-179-5" name="__codelineno-179-5" href="#__codelineno-179-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-179-6" name="__codelineno-179-6" href="#__codelineno-179-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-179-7" name="__codelineno-179-7" href="#__codelineno-179-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-179-8" name="__codelineno-179-8" href="#__codelineno-179-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-179-9" name="__codelineno-179-9" href="#__codelineno-179-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-179-10" name="__codelineno-179-10" href="#__codelineno-179-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-180-1" name="__codelineno-180-1" href="#__codelineno-180-1"></a><span class="cm">/* Линейно-логарифмическая сложность */</span>
<a id="__codelineno-180-2" name="__codelineno-180-2" href="#__codelineno-180-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-180-3" name="__codelineno-180-3" href="#__codelineno-180-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
<a id="__codelineno-180-4" name="__codelineno-180-4" href="#__codelineno-180-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-180-5" name="__codelineno-180-5" href="#__codelineno-180-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
<a id="__codelineno-180-6" name="__codelineno-180-6" href="#__codelineno-180-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-180-7" name="__codelineno-180-7" href="#__codelineno-180-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-180-8" name="__codelineno-180-8" href="#__codelineno-180-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-180-9" name="__codelineno-180-9" href="#__codelineno-180-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-180-10" name="__codelineno-180-10" href="#__codelineno-180-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-181-1" name="__codelineno-181-1" href="#__codelineno-181-1"></a><span class="cm">=begin</span>
<a id="__codelineno-181-2" name="__codelineno-181-2" href="#__codelineno-181-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-181-3" name="__codelineno-181-3" href="#__codelineno-181-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-181-4" name="__codelineno-181-4" href="#__codelineno-181-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-181-5" name="__codelineno-181-5" href="#__codelineno-181-5"></a><span class="cm">=end</span>
<a id="__codelineno-181-6" name="__codelineno-181-6" href="#__codelineno-181-6"></a>
<a id="__codelineno-181-7" name="__codelineno-181-7" href="#__codelineno-181-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-181-8" name="__codelineno-181-8" href="#__codelineno-181-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-9" name="__codelineno-181-9" href="#__codelineno-181-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-181-10" name="__codelineno-181-10" href="#__codelineno-181-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-181-11" name="__codelineno-181-11" href="#__codelineno-181-11"></a>
<a id="__codelineno-181-12" name="__codelineno-181-12" href="#__codelineno-181-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-181-13" name="__codelineno-181-13" href="#__codelineno-181-13"></a>
<a id="__codelineno-181-14" name="__codelineno-181-14" href="#__codelineno-181-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-15" name="__codelineno-181-15" href="#__codelineno-181-15"></a><span class="k">end</span>
<a id="__codelineno-181-16" name="__codelineno-181-16" href="#__codelineno-181-16"></a>
<a id="__codelineno-181-17" name="__codelineno-181-17" href="#__codelineno-181-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-181-18" name="__codelineno-181-18" href="#__codelineno-181-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-19" name="__codelineno-181-19" href="#__codelineno-181-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-181-20" name="__codelineno-181-20" href="#__codelineno-181-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-181-21" name="__codelineno-181-21" href="#__codelineno-181-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-22" name="__codelineno-181-22" href="#__codelineno-181-22"></a><span class="k">end</span>
<a id="__codelineno-181-23" name="__codelineno-181-23" href="#__codelineno-181-23"></a>
<a id="__codelineno-181-24" name="__codelineno-181-24" href="#__codelineno-181-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-181-25" name="__codelineno-181-25" href="#__codelineno-181-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-181-26" name="__codelineno-181-26" href="#__codelineno-181-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-181-27" name="__codelineno-181-27" href="#__codelineno-181-27"></a>
<a id="__codelineno-181-28" name="__codelineno-181-28" href="#__codelineno-181-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-181-29" name="__codelineno-181-29" href="#__codelineno-181-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-181-30" name="__codelineno-181-30" href="#__codelineno-181-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-31" name="__codelineno-181-31" href="#__codelineno-181-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-32" name="__codelineno-181-32" href="#__codelineno-181-32"></a>
<a id="__codelineno-181-33" name="__codelineno-181-33" href="#__codelineno-181-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-34" name="__codelineno-181-34" href="#__codelineno-181-34"></a><span class="k">end</span>
<a id="__codelineno-181-35" name="__codelineno-181-35" href="#__codelineno-181-35"></a>
<a id="__codelineno-181-36" name="__codelineno-181-36" href="#__codelineno-181-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-181-37" name="__codelineno-181-37" href="#__codelineno-181-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-38" name="__codelineno-181-38" href="#__codelineno-181-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-181-39" name="__codelineno-181-39" href="#__codelineno-181-39"></a>
<a id="__codelineno-181-40" name="__codelineno-181-40" href="#__codelineno-181-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-181-41" name="__codelineno-181-41" href="#__codelineno-181-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-181-42" name="__codelineno-181-42" href="#__codelineno-181-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-181-43" name="__codelineno-181-43" href="#__codelineno-181-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-44" name="__codelineno-181-44" href="#__codelineno-181-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-45" name="__codelineno-181-45" href="#__codelineno-181-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-46" name="__codelineno-181-46" href="#__codelineno-181-46"></a>
<a id="__codelineno-181-47" name="__codelineno-181-47" href="#__codelineno-181-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-48" name="__codelineno-181-48" href="#__codelineno-181-48"></a><span class="k">end</span>
<a id="__codelineno-181-49" name="__codelineno-181-49" href="#__codelineno-181-49"></a>
<a id="__codelineno-181-50" name="__codelineno-181-50" href="#__codelineno-181-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-181-51" name="__codelineno-181-51" href="#__codelineno-181-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-181-52" name="__codelineno-181-52" href="#__codelineno-181-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-181-53" name="__codelineno-181-53" href="#__codelineno-181-53"></a>
<a id="__codelineno-181-54" name="__codelineno-181-54" href="#__codelineno-181-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-181-55" name="__codelineno-181-55" href="#__codelineno-181-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-181-56" name="__codelineno-181-56" href="#__codelineno-181-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-181-57" name="__codelineno-181-57" href="#__codelineno-181-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-181-58" name="__codelineno-181-58" href="#__codelineno-181-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-181-59" name="__codelineno-181-59" href="#__codelineno-181-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-181-60" name="__codelineno-181-60" href="#__codelineno-181-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-181-61" name="__codelineno-181-61" href="#__codelineno-181-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-181-62" name="__codelineno-181-62" href="#__codelineno-181-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-181-63" name="__codelineno-181-63" href="#__codelineno-181-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-181-64" name="__codelineno-181-64" href="#__codelineno-181-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-65" name="__codelineno-181-65" href="#__codelineno-181-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-66" name="__codelineno-181-66" href="#__codelineno-181-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-67" name="__codelineno-181-67" href="#__codelineno-181-67"></a>
<a id="__codelineno-181-68" name="__codelineno-181-68" href="#__codelineno-181-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-69" name="__codelineno-181-69" href="#__codelineno-181-69"></a><span class="k">end</span>
<a id="__codelineno-181-70" name="__codelineno-181-70" href="#__codelineno-181-70"></a>
<a id="__codelineno-181-71" name="__codelineno-181-71" href="#__codelineno-181-71"></a><span class="c1"># ## Экспоненциальная сложность (итеративная реализация) ###</span>
<a id="__codelineno-181-72" name="__codelineno-181-72" href="#__codelineno-181-72"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-73" name="__codelineno-181-73" href="#__codelineno-181-73"></a><span class="w"> </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-74" name="__codelineno-181-74" href="#__codelineno-181-74"></a>
<a id="__codelineno-181-75" name="__codelineno-181-75" href="#__codelineno-181-75"></a><span class="w"> </span><span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-181-76" name="__codelineno-181-76" href="#__codelineno-181-76"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-181-77" name="__codelineno-181-77" href="#__codelineno-181-77"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-181-78" name="__codelineno-181-78" href="#__codelineno-181-78"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-181-79" name="__codelineno-181-79" href="#__codelineno-181-79"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-80" name="__codelineno-181-80" href="#__codelineno-181-80"></a>
<a id="__codelineno-181-81" name="__codelineno-181-81" href="#__codelineno-181-81"></a><span class="w"> </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-181-82" name="__codelineno-181-82" href="#__codelineno-181-82"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-83" name="__codelineno-181-83" href="#__codelineno-181-83"></a><span class="k">end</span>
<a id="__codelineno-181-84" name="__codelineno-181-84" href="#__codelineno-181-84"></a>
<a id="__codelineno-181-85" name="__codelineno-181-85" href="#__codelineno-181-85"></a><span class="c1"># ## Экспоненциальная сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-181-86" name="__codelineno-181-86" href="#__codelineno-181-86"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-87" name="__codelineno-181-87" href="#__codelineno-181-87"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-88" name="__codelineno-181-88" href="#__codelineno-181-88"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-89" name="__codelineno-181-89" href="#__codelineno-181-89"></a><span class="k">end</span>
<a id="__codelineno-181-90" name="__codelineno-181-90" href="#__codelineno-181-90"></a>
<a id="__codelineno-181-91" name="__codelineno-181-91" href="#__codelineno-181-91"></a><span class="c1"># ## Логарифмическая сложность (итеративная реализация) ###</span>
<a id="__codelineno-181-92" name="__codelineno-181-92" href="#__codelineno-181-92"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-93" name="__codelineno-181-93" href="#__codelineno-181-93"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-181-94" name="__codelineno-181-94" href="#__codelineno-181-94"></a>
<a id="__codelineno-181-95" name="__codelineno-181-95" href="#__codelineno-181-95"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-96" name="__codelineno-181-96" href="#__codelineno-181-96"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-181-97" name="__codelineno-181-97" href="#__codelineno-181-97"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-98" name="__codelineno-181-98" href="#__codelineno-181-98"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-181-99" name="__codelineno-181-99" href="#__codelineno-181-99"></a>
<a id="__codelineno-181-100" name="__codelineno-181-100" href="#__codelineno-181-100"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-101" name="__codelineno-181-101" href="#__codelineno-181-101"></a><span class="k">end</span>
<a id="__codelineno-181-102" name="__codelineno-181-102" href="#__codelineno-181-102"></a>
<a id="__codelineno-181-103" name="__codelineno-181-103" href="#__codelineno-181-103"></a><span class="c1"># ## Логарифмическая сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-181-104" name="__codelineno-181-104" href="#__codelineno-181-104"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-105" name="__codelineno-181-105" href="#__codelineno-181-105"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-106" name="__codelineno-181-106" href="#__codelineno-181-106"></a><span class="w"> </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-107" name="__codelineno-181-107" href="#__codelineno-181-107"></a><span class="k">end</span>
<a id="__codelineno-181-108" name="__codelineno-181-108" href="#__codelineno-181-108"></a>
<a id="__codelineno-181-109" name="__codelineno-181-109" href="#__codelineno-181-109"></a><span class="c1"># ## Линейно-логарифмическая сложность ###</span>
<a id="__codelineno-181-110" name="__codelineno-181-110" href="#__codelineno-181-110"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-181-111" name="__codelineno-181-111" href="#__codelineno-181-111"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-181-112" name="__codelineno-181-112" href="#__codelineno-181-112"></a>
<a id="__codelineno-181-113" name="__codelineno-181-113" href="#__codelineno-181-113"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-181-114" name="__codelineno-181-114" href="#__codelineno-181-114"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-181-115" name="__codelineno-181-115" href="#__codelineno-181-115"></a>
<a id="__codelineno-181-116" name="__codelineno-181-116" href="#__codelineno-181-116"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-181-117" name="__codelineno-181-117" href="#__codelineno-181-117"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE-%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20%2F%2F%202%29%20%2B%20linear_log_recur%28n%20%2F%2F%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE-%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE-%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20%2F%2F%202%29%20%2B%20linear_log_recur%28n%20%2F%2F%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE-%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p>На рисунке 2-13 показано, как возникает линейно-логарифмическая сложность. Общее число операций на каждом уровне бинарного дерева равно <span class="arithmatex">\(n\)</span> , а дерево имеет <span class="arithmatex">\(\log_2 n + 1\)</span> уровней, поэтому временная сложность равна <span class="arithmatex">\(O(n \log n)\)</span> .</p>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_logarithmic_linear.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Линейно-логарифмическая временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic_linear.png" /></a></p>
<p align="center"> Рисунок 2-13 &nbsp; Линейно-логарифмическая временная сложность </p>
<p>Временная сложность основных алгоритмов сортировки обычно равна <span class="arithmatex">\(O(n \log n)\)</span> , например у быстрой сортировки, сортировки слиянием, пирамидальной сортировки и т.д.</p>
<h3 id="7-on">7. &nbsp; Факториальная сложность <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">&para;</a></h3>
<p>Факториальная сложность соответствует математической задаче "все перестановки". Если даны <span class="arithmatex">\(n\)</span> попарно различных элементов, то число всех возможных перестановок равно:</p>
<div class="arithmatex">\[
n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
\]</div>
<p>Факториал обычно реализуют через рекурсию. Как показано на рисунке 2-14 и в следующем коде, на первом уровне происходит ветвление на <span class="arithmatex">\(n\)</span> подзадач, на втором - на <span class="arithmatex">\(n - 1\)</span> и так далее, пока на <span class="arithmatex">\(n\)</span> -м уровне ветвление не прекращается:</p>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-182-1" name="__codelineno-182-1" href="#__codelineno-182-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-182-2" name="__codelineno-182-2" href="#__codelineno-182-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Факториальная сложность (рекурсивная реализация)&quot;&quot;&quot;</span>
<a id="__codelineno-182-3" name="__codelineno-182-3" href="#__codelineno-182-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<a id="__codelineno-182-4" name="__codelineno-182-4" href="#__codelineno-182-4"></a> <span class="k">return</span> <span class="mi">1</span>
<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a> <span class="c1"># Из одного получается n</span>
<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a> <span class="n">count</span> <span class="o">+=</span> <span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-182-9" name="__codelineno-182-9" href="#__codelineno-182-9"></a> <span class="k">return</span> <span class="n">count</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-183-1" name="__codelineno-183-1" href="#__codelineno-183-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-183-2" name="__codelineno-183-2" href="#__codelineno-183-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-183-3" name="__codelineno-183-3" href="#__codelineno-183-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-183-4" name="__codelineno-183-4" href="#__codelineno-183-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-183-5" name="__codelineno-183-5" href="#__codelineno-183-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-183-6" name="__codelineno-183-6" href="#__codelineno-183-6"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-183-7" name="__codelineno-183-7" href="#__codelineno-183-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-183-8" name="__codelineno-183-8" href="#__codelineno-183-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-183-9" name="__codelineno-183-9" href="#__codelineno-183-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-183-10" name="__codelineno-183-10" href="#__codelineno-183-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-183-11" name="__codelineno-183-11" href="#__codelineno-183-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-184-1" name="__codelineno-184-1" href="#__codelineno-184-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-184-2" name="__codelineno-184-2" href="#__codelineno-184-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-184-3" name="__codelineno-184-3" href="#__codelineno-184-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-184-4" name="__codelineno-184-4" href="#__codelineno-184-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-184-5" name="__codelineno-184-5" href="#__codelineno-184-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-184-6" name="__codelineno-184-6" href="#__codelineno-184-6"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-184-7" name="__codelineno-184-7" href="#__codelineno-184-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-184-8" name="__codelineno-184-8" href="#__codelineno-184-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-184-9" name="__codelineno-184-9" href="#__codelineno-184-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-184-10" name="__codelineno-184-10" href="#__codelineno-184-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-184-11" name="__codelineno-184-11" href="#__codelineno-184-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-185-1" name="__codelineno-185-1" href="#__codelineno-185-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-185-2" name="__codelineno-185-2" href="#__codelineno-185-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">FactorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-185-3" name="__codelineno-185-3" href="#__codelineno-185-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-185-4" name="__codelineno-185-4" href="#__codelineno-185-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-185-5" name="__codelineno-185-5" href="#__codelineno-185-5"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-185-6" name="__codelineno-185-6" href="#__codelineno-185-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-185-7" name="__codelineno-185-7" href="#__codelineno-185-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">FactorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-185-8" name="__codelineno-185-8" href="#__codelineno-185-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-185-9" name="__codelineno-185-9" href="#__codelineno-185-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-185-10" name="__codelineno-185-10" href="#__codelineno-185-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-186-1" name="__codelineno-186-1" href="#__codelineno-186-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-186-2" name="__codelineno-186-2" href="#__codelineno-186-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-186-3" name="__codelineno-186-3" href="#__codelineno-186-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-186-4" name="__codelineno-186-4" href="#__codelineno-186-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-186-5" name="__codelineno-186-5" href="#__codelineno-186-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-186-6" name="__codelineno-186-6" href="#__codelineno-186-6"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-186-7" name="__codelineno-186-7" href="#__codelineno-186-7"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-186-8" name="__codelineno-186-8" href="#__codelineno-186-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-186-9" name="__codelineno-186-9" href="#__codelineno-186-9"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-186-10" name="__codelineno-186-10" href="#__codelineno-186-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-186-11" name="__codelineno-186-11" href="#__codelineno-186-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-186-12" name="__codelineno-186-12" href="#__codelineno-186-12"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-187-1" name="__codelineno-187-1" href="#__codelineno-187-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-187-2" name="__codelineno-187-2" href="#__codelineno-187-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-187-3" name="__codelineno-187-3" href="#__codelineno-187-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-187-4" name="__codelineno-187-4" href="#__codelineno-187-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-187-5" name="__codelineno-187-5" href="#__codelineno-187-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-187-6" name="__codelineno-187-6" href="#__codelineno-187-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-187-7" name="__codelineno-187-7" href="#__codelineno-187-7"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-187-8" name="__codelineno-187-8" href="#__codelineno-187-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-187-9" name="__codelineno-187-9" href="#__codelineno-187-9"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-187-10" name="__codelineno-187-10" href="#__codelineno-187-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-187-11" name="__codelineno-187-11" href="#__codelineno-187-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
<a id="__codelineno-187-12" name="__codelineno-187-12" href="#__codelineno-187-12"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-188-1" name="__codelineno-188-1" href="#__codelineno-188-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-188-2" name="__codelineno-188-2" href="#__codelineno-188-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-188-3" name="__codelineno-188-3" href="#__codelineno-188-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-188-4" name="__codelineno-188-4" href="#__codelineno-188-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-188-5" name="__codelineno-188-5" href="#__codelineno-188-5"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-188-6" name="__codelineno-188-6" href="#__codelineno-188-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-188-7" name="__codelineno-188-7" href="#__codelineno-188-7"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-188-8" name="__codelineno-188-8" href="#__codelineno-188-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-188-9" name="__codelineno-188-9" href="#__codelineno-188-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-188-10" name="__codelineno-188-10" href="#__codelineno-188-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-189-1" name="__codelineno-189-1" href="#__codelineno-189-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-189-2" name="__codelineno-189-2" href="#__codelineno-189-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-189-3" name="__codelineno-189-3" href="#__codelineno-189-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-189-4" name="__codelineno-189-4" href="#__codelineno-189-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-189-5" name="__codelineno-189-5" href="#__codelineno-189-5"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-189-6" name="__codelineno-189-6" href="#__codelineno-189-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-189-7" name="__codelineno-189-7" href="#__codelineno-189-7"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-189-8" name="__codelineno-189-8" href="#__codelineno-189-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-189-9" name="__codelineno-189-9" href="#__codelineno-189-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
<a id="__codelineno-189-10" name="__codelineno-189-10" href="#__codelineno-189-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-190-1" name="__codelineno-190-1" href="#__codelineno-190-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-190-2" name="__codelineno-190-2" href="#__codelineno-190-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-190-3" name="__codelineno-190-3" href="#__codelineno-190-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-190-4" name="__codelineno-190-4" href="#__codelineno-190-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-190-5" name="__codelineno-190-5" href="#__codelineno-190-5"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-190-6" name="__codelineno-190-6" href="#__codelineno-190-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-190-7" name="__codelineno-190-7" href="#__codelineno-190-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-190-8" name="__codelineno-190-8" href="#__codelineno-190-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-190-9" name="__codelineno-190-9" href="#__codelineno-190-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-190-10" name="__codelineno-190-10" href="#__codelineno-190-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-191-1" name="__codelineno-191-1" href="#__codelineno-191-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-191-2" name="__codelineno-191-2" href="#__codelineno-191-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-191-3" name="__codelineno-191-3" href="#__codelineno-191-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-191-4" name="__codelineno-191-4" href="#__codelineno-191-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-191-5" name="__codelineno-191-5" href="#__codelineno-191-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-191-6" name="__codelineno-191-6" href="#__codelineno-191-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-191-7" name="__codelineno-191-7" href="#__codelineno-191-7"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-191-8" name="__codelineno-191-8" href="#__codelineno-191-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-191-9" name="__codelineno-191-9" href="#__codelineno-191-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-191-10" name="__codelineno-191-10" href="#__codelineno-191-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-191-11" name="__codelineno-191-11" href="#__codelineno-191-11"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-191-12" name="__codelineno-191-12" href="#__codelineno-191-12"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-192-1" name="__codelineno-192-1" href="#__codelineno-192-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-192-2" name="__codelineno-192-2" href="#__codelineno-192-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-192-3" name="__codelineno-192-3" href="#__codelineno-192-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-192-4" name="__codelineno-192-4" href="#__codelineno-192-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-192-5" name="__codelineno-192-5" href="#__codelineno-192-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-192-6" name="__codelineno-192-6" href="#__codelineno-192-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-192-7" name="__codelineno-192-7" href="#__codelineno-192-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-192-8" name="__codelineno-192-8" href="#__codelineno-192-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-192-9" name="__codelineno-192-9" href="#__codelineno-192-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-192-10" name="__codelineno-192-10" href="#__codelineno-192-10"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-193-1" name="__codelineno-193-1" href="#__codelineno-193-1"></a><span class="cm">/* Факториальная сложность (рекурсивная реализация) */</span>
<a id="__codelineno-193-2" name="__codelineno-193-2" href="#__codelineno-193-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-193-3" name="__codelineno-193-3" href="#__codelineno-193-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-193-4" name="__codelineno-193-4" href="#__codelineno-193-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-193-5" name="__codelineno-193-5" href="#__codelineno-193-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-193-6" name="__codelineno-193-6" href="#__codelineno-193-6"></a><span class="w"> </span><span class="c1">// Из одного получается n</span>
<a id="__codelineno-193-7" name="__codelineno-193-7" href="#__codelineno-193-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-193-8" name="__codelineno-193-8" href="#__codelineno-193-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
<a id="__codelineno-193-9" name="__codelineno-193-9" href="#__codelineno-193-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-193-10" name="__codelineno-193-10" href="#__codelineno-193-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-193-11" name="__codelineno-193-11" href="#__codelineno-193-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-194-1" name="__codelineno-194-1" href="#__codelineno-194-1"></a><span class="cm">=begin</span>
<a id="__codelineno-194-2" name="__codelineno-194-2" href="#__codelineno-194-2"></a><span class="cm">File: time_complexity.rb</span>
<a id="__codelineno-194-3" name="__codelineno-194-3" href="#__codelineno-194-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-194-4" name="__codelineno-194-4" href="#__codelineno-194-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-194-5" name="__codelineno-194-5" href="#__codelineno-194-5"></a><span class="cm">=end</span>
<a id="__codelineno-194-6" name="__codelineno-194-6" href="#__codelineno-194-6"></a>
<a id="__codelineno-194-7" name="__codelineno-194-7" href="#__codelineno-194-7"></a><span class="c1"># ## Постоянная сложность ###</span>
<a id="__codelineno-194-8" name="__codelineno-194-8" href="#__codelineno-194-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-9" name="__codelineno-194-9" href="#__codelineno-194-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-10" name="__codelineno-194-10" href="#__codelineno-194-10"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
<a id="__codelineno-194-11" name="__codelineno-194-11" href="#__codelineno-194-11"></a>
<a id="__codelineno-194-12" name="__codelineno-194-12" href="#__codelineno-194-12"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-194-13" name="__codelineno-194-13" href="#__codelineno-194-13"></a>
<a id="__codelineno-194-14" name="__codelineno-194-14" href="#__codelineno-194-14"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-15" name="__codelineno-194-15" href="#__codelineno-194-15"></a><span class="k">end</span>
<a id="__codelineno-194-16" name="__codelineno-194-16" href="#__codelineno-194-16"></a>
<a id="__codelineno-194-17" name="__codelineno-194-17" href="#__codelineno-194-17"></a><span class="c1"># ## Линейная сложность ###</span>
<a id="__codelineno-194-18" name="__codelineno-194-18" href="#__codelineno-194-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-19" name="__codelineno-194-19" href="#__codelineno-194-19"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-20" name="__codelineno-194-20" href="#__codelineno-194-20"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-194-21" name="__codelineno-194-21" href="#__codelineno-194-21"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-22" name="__codelineno-194-22" href="#__codelineno-194-22"></a><span class="k">end</span>
<a id="__codelineno-194-23" name="__codelineno-194-23" href="#__codelineno-194-23"></a>
<a id="__codelineno-194-24" name="__codelineno-194-24" href="#__codelineno-194-24"></a><span class="c1"># ## Линейная сложность (обход массива) ###</span>
<a id="__codelineno-194-25" name="__codelineno-194-25" href="#__codelineno-194-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-194-26" name="__codelineno-194-26" href="#__codelineno-194-26"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-27" name="__codelineno-194-27" href="#__codelineno-194-27"></a>
<a id="__codelineno-194-28" name="__codelineno-194-28" href="#__codelineno-194-28"></a><span class="w"> </span><span class="c1"># Число итераций пропорционально длине массива</span>
<a id="__codelineno-194-29" name="__codelineno-194-29" href="#__codelineno-194-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-194-30" name="__codelineno-194-30" href="#__codelineno-194-30"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-31" name="__codelineno-194-31" href="#__codelineno-194-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-32" name="__codelineno-194-32" href="#__codelineno-194-32"></a>
<a id="__codelineno-194-33" name="__codelineno-194-33" href="#__codelineno-194-33"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-34" name="__codelineno-194-34" href="#__codelineno-194-34"></a><span class="k">end</span>
<a id="__codelineno-194-35" name="__codelineno-194-35" href="#__codelineno-194-35"></a>
<a id="__codelineno-194-36" name="__codelineno-194-36" href="#__codelineno-194-36"></a><span class="c1"># ## Квадратичная сложность ###</span>
<a id="__codelineno-194-37" name="__codelineno-194-37" href="#__codelineno-194-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-38" name="__codelineno-194-38" href="#__codelineno-194-38"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-39" name="__codelineno-194-39" href="#__codelineno-194-39"></a>
<a id="__codelineno-194-40" name="__codelineno-194-40" href="#__codelineno-194-40"></a><span class="w"> </span><span class="c1"># Число итераций квадратично зависит от размера данных n</span>
<a id="__codelineno-194-41" name="__codelineno-194-41" href="#__codelineno-194-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-194-42" name="__codelineno-194-42" href="#__codelineno-194-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
<a id="__codelineno-194-43" name="__codelineno-194-43" href="#__codelineno-194-43"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-44" name="__codelineno-194-44" href="#__codelineno-194-44"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-45" name="__codelineno-194-45" href="#__codelineno-194-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-46" name="__codelineno-194-46" href="#__codelineno-194-46"></a>
<a id="__codelineno-194-47" name="__codelineno-194-47" href="#__codelineno-194-47"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-48" name="__codelineno-194-48" href="#__codelineno-194-48"></a><span class="k">end</span>
<a id="__codelineno-194-49" name="__codelineno-194-49" href="#__codelineno-194-49"></a>
<a id="__codelineno-194-50" name="__codelineno-194-50" href="#__codelineno-194-50"></a><span class="c1"># ## Квадратичная сложность (пузырьковая сортировка) ###</span>
<a id="__codelineno-194-51" name="__codelineno-194-51" href="#__codelineno-194-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-194-52" name="__codelineno-194-52" href="#__codelineno-194-52"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># Счетчик</span>
<a id="__codelineno-194-53" name="__codelineno-194-53" href="#__codelineno-194-53"></a>
<a id="__codelineno-194-54" name="__codelineno-194-54" href="#__codelineno-194-54"></a><span class="w"> </span><span class="c1"># Внешний цикл: неотсортированный диапазон [0, i]</span>
<a id="__codelineno-194-55" name="__codelineno-194-55" href="#__codelineno-194-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-194-56" name="__codelineno-194-56" href="#__codelineno-194-56"></a><span class="w"> </span><span class="c1"># Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец</span>
<a id="__codelineno-194-57" name="__codelineno-194-57" href="#__codelineno-194-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
<a id="__codelineno-194-58" name="__codelineno-194-58" href="#__codelineno-194-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-194-59" name="__codelineno-194-59" href="#__codelineno-194-59"></a><span class="w"> </span><span class="c1"># Поменять местами nums[j] и nums[j + 1]</span>
<a id="__codelineno-194-60" name="__codelineno-194-60" href="#__codelineno-194-60"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a id="__codelineno-194-61" name="__codelineno-194-61" href="#__codelineno-194-61"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a id="__codelineno-194-62" name="__codelineno-194-62" href="#__codelineno-194-62"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
<a id="__codelineno-194-63" name="__codelineno-194-63" href="#__codelineno-194-63"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># Обмен элементов включает 3 элементарные операции</span>
<a id="__codelineno-194-64" name="__codelineno-194-64" href="#__codelineno-194-64"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-65" name="__codelineno-194-65" href="#__codelineno-194-65"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-66" name="__codelineno-194-66" href="#__codelineno-194-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-67" name="__codelineno-194-67" href="#__codelineno-194-67"></a>
<a id="__codelineno-194-68" name="__codelineno-194-68" href="#__codelineno-194-68"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-69" name="__codelineno-194-69" href="#__codelineno-194-69"></a><span class="k">end</span>
<a id="__codelineno-194-70" name="__codelineno-194-70" href="#__codelineno-194-70"></a>
<a id="__codelineno-194-71" name="__codelineno-194-71" href="#__codelineno-194-71"></a><span class="c1"># ## Экспоненциальная сложность (итеративная реализация) ###</span>
<a id="__codelineno-194-72" name="__codelineno-194-72" href="#__codelineno-194-72"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-73" name="__codelineno-194-73" href="#__codelineno-194-73"></a><span class="w"> </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-74" name="__codelineno-194-74" href="#__codelineno-194-74"></a>
<a id="__codelineno-194-75" name="__codelineno-194-75" href="#__codelineno-194-75"></a><span class="w"> </span><span class="c1"># На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)</span>
<a id="__codelineno-194-76" name="__codelineno-194-76" href="#__codelineno-194-76"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
<a id="__codelineno-194-77" name="__codelineno-194-77" href="#__codelineno-194-77"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-194-78" name="__codelineno-194-78" href="#__codelineno-194-78"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-194-79" name="__codelineno-194-79" href="#__codelineno-194-79"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-80" name="__codelineno-194-80" href="#__codelineno-194-80"></a>
<a id="__codelineno-194-81" name="__codelineno-194-81" href="#__codelineno-194-81"></a><span class="w"> </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-194-82" name="__codelineno-194-82" href="#__codelineno-194-82"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-83" name="__codelineno-194-83" href="#__codelineno-194-83"></a><span class="k">end</span>
<a id="__codelineno-194-84" name="__codelineno-194-84" href="#__codelineno-194-84"></a>
<a id="__codelineno-194-85" name="__codelineno-194-85" href="#__codelineno-194-85"></a><span class="c1"># ## Экспоненциальная сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-194-86" name="__codelineno-194-86" href="#__codelineno-194-86"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-87" name="__codelineno-194-87" href="#__codelineno-194-87"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-88" name="__codelineno-194-88" href="#__codelineno-194-88"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-89" name="__codelineno-194-89" href="#__codelineno-194-89"></a><span class="k">end</span>
<a id="__codelineno-194-90" name="__codelineno-194-90" href="#__codelineno-194-90"></a>
<a id="__codelineno-194-91" name="__codelineno-194-91" href="#__codelineno-194-91"></a><span class="c1"># ## Логарифмическая сложность (итеративная реализация) ###</span>
<a id="__codelineno-194-92" name="__codelineno-194-92" href="#__codelineno-194-92"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-93" name="__codelineno-194-93" href="#__codelineno-194-93"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-94" name="__codelineno-194-94" href="#__codelineno-194-94"></a>
<a id="__codelineno-194-95" name="__codelineno-194-95" href="#__codelineno-194-95"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-96" name="__codelineno-194-96" href="#__codelineno-194-96"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-194-97" name="__codelineno-194-97" href="#__codelineno-194-97"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-98" name="__codelineno-194-98" href="#__codelineno-194-98"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-194-99" name="__codelineno-194-99" href="#__codelineno-194-99"></a>
<a id="__codelineno-194-100" name="__codelineno-194-100" href="#__codelineno-194-100"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-101" name="__codelineno-194-101" href="#__codelineno-194-101"></a><span class="k">end</span>
<a id="__codelineno-194-102" name="__codelineno-194-102" href="#__codelineno-194-102"></a>
<a id="__codelineno-194-103" name="__codelineno-194-103" href="#__codelineno-194-103"></a><span class="c1"># ## Логарифмическая сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-194-104" name="__codelineno-194-104" href="#__codelineno-194-104"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-105" name="__codelineno-194-105" href="#__codelineno-194-105"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-106" name="__codelineno-194-106" href="#__codelineno-194-106"></a><span class="w"> </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-107" name="__codelineno-194-107" href="#__codelineno-194-107"></a><span class="k">end</span>
<a id="__codelineno-194-108" name="__codelineno-194-108" href="#__codelineno-194-108"></a>
<a id="__codelineno-194-109" name="__codelineno-194-109" href="#__codelineno-194-109"></a><span class="c1"># ## Линейно-логарифмическая сложность ###</span>
<a id="__codelineno-194-110" name="__codelineno-194-110" href="#__codelineno-194-110"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-111" name="__codelineno-194-111" href="#__codelineno-194-111"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-194-112" name="__codelineno-194-112" href="#__codelineno-194-112"></a>
<a id="__codelineno-194-113" name="__codelineno-194-113" href="#__codelineno-194-113"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-194-114" name="__codelineno-194-114" href="#__codelineno-194-114"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-194-115" name="__codelineno-194-115" href="#__codelineno-194-115"></a>
<a id="__codelineno-194-116" name="__codelineno-194-116" href="#__codelineno-194-116"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-117" name="__codelineno-194-117" href="#__codelineno-194-117"></a><span class="k">end</span>
<a id="__codelineno-194-118" name="__codelineno-194-118" href="#__codelineno-194-118"></a>
<a id="__codelineno-194-119" name="__codelineno-194-119" href="#__codelineno-194-119"></a><span class="c1"># ## Факториальная сложность (рекурсивная реализация) ###</span>
<a id="__codelineno-194-120" name="__codelineno-194-120" href="#__codelineno-194-120"></a><span class="k">def</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-194-121" name="__codelineno-194-121" href="#__codelineno-194-121"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-122" name="__codelineno-194-122" href="#__codelineno-194-122"></a>
<a id="__codelineno-194-123" name="__codelineno-194-123" href="#__codelineno-194-123"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-194-124" name="__codelineno-194-124" href="#__codelineno-194-124"></a><span class="w"> </span><span class="c1"># Из одного получается n</span>
<a id="__codelineno-194-125" name="__codelineno-194-125" href="#__codelineno-194-125"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-194-126" name="__codelineno-194-126" href="#__codelineno-194-126"></a>
<a id="__codelineno-194-127" name="__codelineno-194-127" href="#__codelineno-194-127"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-194-128" name="__codelineno-194-128" href="#__codelineno-194-128"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Визуализация кода</summary>
<p><div style="height: 495px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20factorial_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%98%D0%B7%20%D0%BE%D0%B4%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%B0%D0%B5%D1%82%D1%81%D1%8F%20n%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20factorial_recur%28n%20-%201%29%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20factorial_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%84%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20factorial_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%98%D0%B7%20%D0%BE%D0%B4%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%B0%D0%B5%D1%82%D1%81%D1%8F%20n%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20factorial_recur%28n%20-%201%29%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20factorial_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%84%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
</details>
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_factorial.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Факториальная временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_factorial.png" /></a></p>
<p align="center"> Рисунок 2-14 &nbsp; Факториальная временная сложность </p>
<p>Обрати внимание: поскольку при <span class="arithmatex">\(n \geq 4\)</span> всегда выполняется <span class="arithmatex">\(n! &gt; 2^n\)</span> , факториальная сложность растет еще быстрее, чем экспоненциальная, и при больших <span class="arithmatex">\(n\)</span> также неприемлема.</p>
<h2 id="235">2.3.5 &nbsp; Худшая, лучшая и средняя временная сложность<a class="headerlink" href="#235" title="Permanent link">&para;</a></h2>
<p><strong>Временная эффективность алгоритма часто не фиксирована, а зависит от распределения входных данных</strong>. Предположим, на вход подается массив <code>nums</code> длины <span class="arithmatex">\(n\)</span> , состоящий из чисел от <span class="arithmatex">\(1\)</span> до <span class="arithmatex">\(n\)</span> , каждое из которых встречается ровно один раз; при этом порядок элементов случайно перемешан. Задача состоит в том, чтобы вернуть индекс элемента <span class="arithmatex">\(1\)</span> . Тогда можно сделать следующие выводы.</p>
<ul>
<li>Когда <code>nums = [?, ?, ..., 1]</code> , то есть когда последний элемент равен <span class="arithmatex">\(1\)</span> , нужно полностью пройти по массиву, <strong>что дает худшую временную сложность <span class="arithmatex">\(O(n)\)</span></strong> .</li>
<li>Когда <code>nums = [1, ?, ?, ...]</code> , то есть когда первый элемент равен <span class="arithmatex">\(1\)</span> , независимо от длины массива продолжать обход не нужно, <strong>что дает лучшую временную сложность <span class="arithmatex">\(\Omega(1)\)</span></strong> .</li>
</ul>
<p>"Худшая временная сложность" соответствует асимптотической верхней границе функции и обозначается нотацией Big <span class="arithmatex">\(O\)</span> . Соответственно, "лучшая временная сложность" соответствует асимптотической нижней границе функции и обозначается символом <span class="arithmatex">\(\Omega\)</span> :</p>
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<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-195-1" name="__codelineno-195-1" href="#__codelineno-195-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<a id="__codelineno-195-2" name="__codelineno-195-2" href="#__codelineno-195-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Сгенерировать массив с элементами 1, 2, ..., n в случайном порядке&quot;&quot;&quot;</span>
<a id="__codelineno-195-3" name="__codelineno-195-3" href="#__codelineno-195-3"></a> <span class="c1"># Создать массив nums =: 1, 2, 3, ..., n</span>
<a id="__codelineno-195-4" name="__codelineno-195-4" href="#__codelineno-195-4"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
<a id="__codelineno-195-5" name="__codelineno-195-5" href="#__codelineno-195-5"></a> <span class="c1"># Случайно перемешать элементы массива</span>
<a id="__codelineno-195-6" name="__codelineno-195-6" href="#__codelineno-195-6"></a> <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-195-7" name="__codelineno-195-7" href="#__codelineno-195-7"></a> <span class="k">return</span> <span class="n">nums</span>
<a id="__codelineno-195-8" name="__codelineno-195-8" href="#__codelineno-195-8"></a>
<a id="__codelineno-195-9" name="__codelineno-195-9" href="#__codelineno-195-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-195-10" name="__codelineno-195-10" href="#__codelineno-195-10"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Найти индекс числа 1 в массиве nums&quot;&quot;&quot;</span>
<a id="__codelineno-195-11" name="__codelineno-195-11" href="#__codelineno-195-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
<a id="__codelineno-195-12" name="__codelineno-195-12" href="#__codelineno-195-12"></a> <span class="c1"># Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-195-13" name="__codelineno-195-13" href="#__codelineno-195-13"></a> <span class="c1"># Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-195-14" name="__codelineno-195-14" href="#__codelineno-195-14"></a> <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<a id="__codelineno-195-15" name="__codelineno-195-15" href="#__codelineno-195-15"></a> <span class="k">return</span> <span class="n">i</span>
<a id="__codelineno-195-16" name="__codelineno-195-16" href="#__codelineno-195-16"></a> <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-196-1" name="__codelineno-196-1" href="#__codelineno-196-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-196-2" name="__codelineno-196-2" href="#__codelineno-196-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-196-3" name="__codelineno-196-3" href="#__codelineno-196-3"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
<a id="__codelineno-196-4" name="__codelineno-196-4" href="#__codelineno-196-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-196-5" name="__codelineno-196-5" href="#__codelineno-196-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-196-6" name="__codelineno-196-6" href="#__codelineno-196-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-196-7" name="__codelineno-196-7" href="#__codelineno-196-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-196-8" name="__codelineno-196-8" href="#__codelineno-196-8"></a><span class="w"> </span><span class="c1">// Использовать системное время для генерации случайного seed</span>
<a id="__codelineno-196-9" name="__codelineno-196-9" href="#__codelineno-196-9"></a><span class="w"> </span><span class="kt">unsigned</span><span class="w"> </span><span class="n">seed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">chrono</span><span class="o">::</span><span class="n">system_clock</span><span class="o">::</span><span class="n">now</span><span class="p">().</span><span class="n">time_since_epoch</span><span class="p">().</span><span class="n">count</span><span class="p">();</span>
<a id="__codelineno-196-10" name="__codelineno-196-10" href="#__codelineno-196-10"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-196-11" name="__codelineno-196-11" href="#__codelineno-196-11"></a><span class="w"> </span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">default_random_engine</span><span class="p">(</span><span class="n">seed</span><span class="p">));</span>
<a id="__codelineno-196-12" name="__codelineno-196-12" href="#__codelineno-196-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
<a id="__codelineno-196-13" name="__codelineno-196-13" href="#__codelineno-196-13"></a><span class="p">}</span>
<a id="__codelineno-196-14" name="__codelineno-196-14" href="#__codelineno-196-14"></a>
<a id="__codelineno-196-15" name="__codelineno-196-15" href="#__codelineno-196-15"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-196-16" name="__codelineno-196-16" href="#__codelineno-196-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-196-17" name="__codelineno-196-17" href="#__codelineno-196-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-196-18" name="__codelineno-196-18" href="#__codelineno-196-18"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-196-19" name="__codelineno-196-19" href="#__codelineno-196-19"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-196-20" name="__codelineno-196-20" href="#__codelineno-196-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-196-21" name="__codelineno-196-21" href="#__codelineno-196-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-196-22" name="__codelineno-196-22" href="#__codelineno-196-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-196-23" name="__codelineno-196-23" href="#__codelineno-196-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
<a id="__codelineno-196-24" name="__codelineno-196-24" href="#__codelineno-196-24"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.java</span><pre><span></span><code><a id="__codelineno-197-1" name="__codelineno-197-1" href="#__codelineno-197-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-197-2" name="__codelineno-197-2" href="#__codelineno-197-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-197-3" name="__codelineno-197-3" href="#__codelineno-197-3"></a><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
<a id="__codelineno-197-4" name="__codelineno-197-4" href="#__codelineno-197-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-197-5" name="__codelineno-197-5" href="#__codelineno-197-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-197-6" name="__codelineno-197-6" href="#__codelineno-197-6"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-197-7" name="__codelineno-197-7" href="#__codelineno-197-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-197-8" name="__codelineno-197-8" href="#__codelineno-197-8"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-197-9" name="__codelineno-197-9" href="#__codelineno-197-9"></a><span class="w"> </span><span class="n">Collections</span><span class="p">.</span><span class="na">shuffle</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
<a id="__codelineno-197-10" name="__codelineno-197-10" href="#__codelineno-197-10"></a><span class="w"> </span><span class="c1">// Integer[] -&gt; int[]</span>
<a id="__codelineno-197-11" name="__codelineno-197-11" href="#__codelineno-197-11"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
<a id="__codelineno-197-12" name="__codelineno-197-12" href="#__codelineno-197-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-197-13" name="__codelineno-197-13" href="#__codelineno-197-13"></a><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
<a id="__codelineno-197-14" name="__codelineno-197-14" href="#__codelineno-197-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-197-15" name="__codelineno-197-15" href="#__codelineno-197-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a id="__codelineno-197-16" name="__codelineno-197-16" href="#__codelineno-197-16"></a><span class="p">}</span>
<a id="__codelineno-197-17" name="__codelineno-197-17" href="#__codelineno-197-17"></a>
<a id="__codelineno-197-18" name="__codelineno-197-18" href="#__codelineno-197-18"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-197-19" name="__codelineno-197-19" href="#__codelineno-197-19"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-197-20" name="__codelineno-197-20" href="#__codelineno-197-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-197-21" name="__codelineno-197-21" href="#__codelineno-197-21"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-197-22" name="__codelineno-197-22" href="#__codelineno-197-22"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-197-23" name="__codelineno-197-23" href="#__codelineno-197-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-197-24" name="__codelineno-197-24" href="#__codelineno-197-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-197-25" name="__codelineno-197-25" href="#__codelineno-197-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-197-26" name="__codelineno-197-26" href="#__codelineno-197-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-197-27" name="__codelineno-197-27" href="#__codelineno-197-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.cs</span><pre><span></span><code><a id="__codelineno-198-1" name="__codelineno-198-1" href="#__codelineno-198-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-198-2" name="__codelineno-198-2" href="#__codelineno-198-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">RandomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-198-3" name="__codelineno-198-3" href="#__codelineno-198-3"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
<a id="__codelineno-198-4" name="__codelineno-198-4" href="#__codelineno-198-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-198-5" name="__codelineno-198-5" href="#__codelineno-198-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-198-6" name="__codelineno-198-6" href="#__codelineno-198-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-198-7" name="__codelineno-198-7" href="#__codelineno-198-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-198-8" name="__codelineno-198-8" href="#__codelineno-198-8"></a>
<a id="__codelineno-198-9" name="__codelineno-198-9" href="#__codelineno-198-9"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-198-10" name="__codelineno-198-10" href="#__codelineno-198-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-198-11" name="__codelineno-198-11" href="#__codelineno-198-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Random</span><span class="p">().</span><span class="n">Next</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">);</span>
<a id="__codelineno-198-12" name="__codelineno-198-12" href="#__codelineno-198-12"></a><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<a id="__codelineno-198-13" name="__codelineno-198-13" href="#__codelineno-198-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-198-14" name="__codelineno-198-14" href="#__codelineno-198-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
<a id="__codelineno-198-15" name="__codelineno-198-15" href="#__codelineno-198-15"></a><span class="p">}</span>
<a id="__codelineno-198-16" name="__codelineno-198-16" href="#__codelineno-198-16"></a>
<a id="__codelineno-198-17" name="__codelineno-198-17" href="#__codelineno-198-17"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-198-18" name="__codelineno-198-18" href="#__codelineno-198-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">FindOne</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-198-19" name="__codelineno-198-19" href="#__codelineno-198-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-198-20" name="__codelineno-198-20" href="#__codelineno-198-20"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-198-21" name="__codelineno-198-21" href="#__codelineno-198-21"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-198-22" name="__codelineno-198-22" href="#__codelineno-198-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-198-23" name="__codelineno-198-23" href="#__codelineno-198-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-198-24" name="__codelineno-198-24" href="#__codelineno-198-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-198-25" name="__codelineno-198-25" href="#__codelineno-198-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-198-26" name="__codelineno-198-26" href="#__codelineno-198-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.go</span><pre><span></span><code><a id="__codelineno-199-1" name="__codelineno-199-1" href="#__codelineno-199-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-199-2" name="__codelineno-199-2" href="#__codelineno-199-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-199-3" name="__codelineno-199-3" href="#__codelineno-199-3"></a><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
<a id="__codelineno-199-4" name="__codelineno-199-4" href="#__codelineno-199-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-199-5" name="__codelineno-199-5" href="#__codelineno-199-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-199-6" name="__codelineno-199-6" href="#__codelineno-199-6"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-199-7" name="__codelineno-199-7" href="#__codelineno-199-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-199-8" name="__codelineno-199-8" href="#__codelineno-199-8"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-199-9" name="__codelineno-199-9" href="#__codelineno-199-9"></a><span class="w"> </span><span class="nx">rand</span><span class="p">.</span><span class="nx">Shuffle</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">),</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-199-10" name="__codelineno-199-10" href="#__codelineno-199-10"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-199-11" name="__codelineno-199-11" href="#__codelineno-199-11"></a><span class="w"> </span><span class="p">})</span>
<a id="__codelineno-199-12" name="__codelineno-199-12" href="#__codelineno-199-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span>
<a id="__codelineno-199-13" name="__codelineno-199-13" href="#__codelineno-199-13"></a><span class="p">}</span>
<a id="__codelineno-199-14" name="__codelineno-199-14" href="#__codelineno-199-14"></a>
<a id="__codelineno-199-15" name="__codelineno-199-15" href="#__codelineno-199-15"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-199-16" name="__codelineno-199-16" href="#__codelineno-199-16"></a><span class="kd">func</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-199-17" name="__codelineno-199-17" href="#__codelineno-199-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-199-18" name="__codelineno-199-18" href="#__codelineno-199-18"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-199-19" name="__codelineno-199-19" href="#__codelineno-199-19"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-199-20" name="__codelineno-199-20" href="#__codelineno-199-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-199-21" name="__codelineno-199-21" href="#__codelineno-199-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-199-22" name="__codelineno-199-22" href="#__codelineno-199-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-199-23" name="__codelineno-199-23" href="#__codelineno-199-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-199-24" name="__codelineno-199-24" href="#__codelineno-199-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-199-25" name="__codelineno-199-25" href="#__codelineno-199-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.swift</span><pre><span></span><code><a id="__codelineno-200-1" name="__codelineno-200-1" href="#__codelineno-200-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-200-2" name="__codelineno-200-2" href="#__codelineno-200-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-200-3" name="__codelineno-200-3" href="#__codelineno-200-3"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-200-4" name="__codelineno-200-4" href="#__codelineno-200-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-200-5" name="__codelineno-200-5" href="#__codelineno-200-5"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-200-6" name="__codelineno-200-6" href="#__codelineno-200-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">()</span>
<a id="__codelineno-200-7" name="__codelineno-200-7" href="#__codelineno-200-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-200-8" name="__codelineno-200-8" href="#__codelineno-200-8"></a><span class="p">}</span>
<a id="__codelineno-200-9" name="__codelineno-200-9" href="#__codelineno-200-9"></a>
<a id="__codelineno-200-10" name="__codelineno-200-10" href="#__codelineno-200-10"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-200-11" name="__codelineno-200-11" href="#__codelineno-200-11"></a><span class="kd">func</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-200-12" name="__codelineno-200-12" href="#__codelineno-200-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-200-13" name="__codelineno-200-13" href="#__codelineno-200-13"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-200-14" name="__codelineno-200-14" href="#__codelineno-200-14"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-200-15" name="__codelineno-200-15" href="#__codelineno-200-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-200-16" name="__codelineno-200-16" href="#__codelineno-200-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
<a id="__codelineno-200-17" name="__codelineno-200-17" href="#__codelineno-200-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-200-18" name="__codelineno-200-18" href="#__codelineno-200-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-200-19" name="__codelineno-200-19" href="#__codelineno-200-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-200-20" name="__codelineno-200-20" href="#__codelineno-200-20"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.js</span><pre><span></span><code><a id="__codelineno-201-1" name="__codelineno-201-1" href="#__codelineno-201-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-201-2" name="__codelineno-201-2" href="#__codelineno-201-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-201-3" name="__codelineno-201-3" href="#__codelineno-201-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
<a id="__codelineno-201-4" name="__codelineno-201-4" href="#__codelineno-201-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-201-5" name="__codelineno-201-5" href="#__codelineno-201-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-201-6" name="__codelineno-201-6" href="#__codelineno-201-6"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-201-7" name="__codelineno-201-7" href="#__codelineno-201-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-201-8" name="__codelineno-201-8" href="#__codelineno-201-8"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-201-9" name="__codelineno-201-9" href="#__codelineno-201-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-201-10" name="__codelineno-201-10" href="#__codelineno-201-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
<a id="__codelineno-201-11" name="__codelineno-201-11" href="#__codelineno-201-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
<a id="__codelineno-201-12" name="__codelineno-201-12" href="#__codelineno-201-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">];</span>
<a id="__codelineno-201-13" name="__codelineno-201-13" href="#__codelineno-201-13"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span>
<a id="__codelineno-201-14" name="__codelineno-201-14" href="#__codelineno-201-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-201-15" name="__codelineno-201-15" href="#__codelineno-201-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span><span class="p">;</span>
<a id="__codelineno-201-16" name="__codelineno-201-16" href="#__codelineno-201-16"></a><span class="p">}</span>
<a id="__codelineno-201-17" name="__codelineno-201-17" href="#__codelineno-201-17"></a>
<a id="__codelineno-201-18" name="__codelineno-201-18" href="#__codelineno-201-18"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-201-19" name="__codelineno-201-19" href="#__codelineno-201-19"></a><span class="kd">function</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-201-20" name="__codelineno-201-20" href="#__codelineno-201-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-201-21" name="__codelineno-201-21" href="#__codelineno-201-21"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-201-22" name="__codelineno-201-22" href="#__codelineno-201-22"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-201-23" name="__codelineno-201-23" href="#__codelineno-201-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-201-24" name="__codelineno-201-24" href="#__codelineno-201-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
<a id="__codelineno-201-25" name="__codelineno-201-25" href="#__codelineno-201-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-201-26" name="__codelineno-201-26" href="#__codelineno-201-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-201-27" name="__codelineno-201-27" href="#__codelineno-201-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-201-28" name="__codelineno-201-28" href="#__codelineno-201-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.ts</span><pre><span></span><code><a id="__codelineno-202-1" name="__codelineno-202-1" href="#__codelineno-202-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-202-2" name="__codelineno-202-2" href="#__codelineno-202-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-202-3" name="__codelineno-202-3" href="#__codelineno-202-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
<a id="__codelineno-202-4" name="__codelineno-202-4" href="#__codelineno-202-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-202-5" name="__codelineno-202-5" href="#__codelineno-202-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-202-6" name="__codelineno-202-6" href="#__codelineno-202-6"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-202-7" name="__codelineno-202-7" href="#__codelineno-202-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-202-8" name="__codelineno-202-8" href="#__codelineno-202-8"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-202-9" name="__codelineno-202-9" href="#__codelineno-202-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-202-10" name="__codelineno-202-10" href="#__codelineno-202-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
<a id="__codelineno-202-11" name="__codelineno-202-11" href="#__codelineno-202-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
<a id="__codelineno-202-12" name="__codelineno-202-12" href="#__codelineno-202-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">];</span>
<a id="__codelineno-202-13" name="__codelineno-202-13" href="#__codelineno-202-13"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span>
<a id="__codelineno-202-14" name="__codelineno-202-14" href="#__codelineno-202-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-202-15" name="__codelineno-202-15" href="#__codelineno-202-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span><span class="p">;</span>
<a id="__codelineno-202-16" name="__codelineno-202-16" href="#__codelineno-202-16"></a><span class="p">}</span>
<a id="__codelineno-202-17" name="__codelineno-202-17" href="#__codelineno-202-17"></a>
<a id="__codelineno-202-18" name="__codelineno-202-18" href="#__codelineno-202-18"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-202-19" name="__codelineno-202-19" href="#__codelineno-202-19"></a><span class="kd">function</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-202-20" name="__codelineno-202-20" href="#__codelineno-202-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-202-21" name="__codelineno-202-21" href="#__codelineno-202-21"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-202-22" name="__codelineno-202-22" href="#__codelineno-202-22"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-202-23" name="__codelineno-202-23" href="#__codelineno-202-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-202-24" name="__codelineno-202-24" href="#__codelineno-202-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
<a id="__codelineno-202-25" name="__codelineno-202-25" href="#__codelineno-202-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-202-26" name="__codelineno-202-26" href="#__codelineno-202-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-202-27" name="__codelineno-202-27" href="#__codelineno-202-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-202-28" name="__codelineno-202-28" href="#__codelineno-202-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.dart</span><pre><span></span><code><a id="__codelineno-203-1" name="__codelineno-203-1" href="#__codelineno-203-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-203-2" name="__codelineno-203-2" href="#__codelineno-203-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-203-3" name="__codelineno-203-3" href="#__codelineno-203-3"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-203-4" name="__codelineno-203-4" href="#__codelineno-203-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-203-5" name="__codelineno-203-5" href="#__codelineno-203-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-203-6" name="__codelineno-203-6" href="#__codelineno-203-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-203-7" name="__codelineno-203-7" href="#__codelineno-203-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-203-8" name="__codelineno-203-8" href="#__codelineno-203-8"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-203-9" name="__codelineno-203-9" href="#__codelineno-203-9"></a><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">();</span>
<a id="__codelineno-203-10" name="__codelineno-203-10" href="#__codelineno-203-10"></a>
<a id="__codelineno-203-11" name="__codelineno-203-11" href="#__codelineno-203-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
<a id="__codelineno-203-12" name="__codelineno-203-12" href="#__codelineno-203-12"></a><span class="p">}</span>
<a id="__codelineno-203-13" name="__codelineno-203-13" href="#__codelineno-203-13"></a>
<a id="__codelineno-203-14" name="__codelineno-203-14" href="#__codelineno-203-14"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-203-15" name="__codelineno-203-15" href="#__codelineno-203-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-203-16" name="__codelineno-203-16" href="#__codelineno-203-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-203-17" name="__codelineno-203-17" href="#__codelineno-203-17"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-203-18" name="__codelineno-203-18" href="#__codelineno-203-18"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-203-19" name="__codelineno-203-19" href="#__codelineno-203-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-203-20" name="__codelineno-203-20" href="#__codelineno-203-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-203-21" name="__codelineno-203-21" href="#__codelineno-203-21"></a>
<a id="__codelineno-203-22" name="__codelineno-203-22" href="#__codelineno-203-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-203-23" name="__codelineno-203-23" href="#__codelineno-203-23"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.rs</span><pre><span></span><code><a id="__codelineno-204-1" name="__codelineno-204-1" href="#__codelineno-204-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-204-2" name="__codelineno-204-2" href="#__codelineno-204-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-204-3" name="__codelineno-204-3" href="#__codelineno-204-3"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-204-4" name="__codelineno-204-4" href="#__codelineno-204-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="p">).</span><span class="n">collect</span><span class="p">::</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">();</span>
<a id="__codelineno-204-5" name="__codelineno-204-5" href="#__codelineno-204-5"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-204-6" name="__codelineno-204-6" href="#__codelineno-204-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">thread_rng</span><span class="p">());</span>
<a id="__codelineno-204-7" name="__codelineno-204-7" href="#__codelineno-204-7"></a><span class="w"> </span><span class="n">nums</span>
<a id="__codelineno-204-8" name="__codelineno-204-8" href="#__codelineno-204-8"></a><span class="p">}</span>
<a id="__codelineno-204-9" name="__codelineno-204-9" href="#__codelineno-204-9"></a>
<a id="__codelineno-204-10" name="__codelineno-204-10" href="#__codelineno-204-10"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-204-11" name="__codelineno-204-11" href="#__codelineno-204-11"></a><span class="k">fn</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">usize</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-204-12" name="__codelineno-204-12" href="#__codelineno-204-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-204-13" name="__codelineno-204-13" href="#__codelineno-204-13"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-204-14" name="__codelineno-204-14" href="#__codelineno-204-14"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-204-15" name="__codelineno-204-15" href="#__codelineno-204-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-204-16" name="__codelineno-204-16" href="#__codelineno-204-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-204-17" name="__codelineno-204-17" href="#__codelineno-204-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-204-18" name="__codelineno-204-18" href="#__codelineno-204-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-204-19" name="__codelineno-204-19" href="#__codelineno-204-19"></a><span class="w"> </span><span class="nb">None</span>
<a id="__codelineno-204-20" name="__codelineno-204-20" href="#__codelineno-204-20"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.c</span><pre><span></span><code><a id="__codelineno-205-1" name="__codelineno-205-1" href="#__codelineno-205-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-205-2" name="__codelineno-205-2" href="#__codelineno-205-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-205-3" name="__codelineno-205-3" href="#__codelineno-205-3"></a><span class="w"> </span><span class="c1">// Выделить память в куче (создать одномерный массив переменной длины: число элементов равно n, тип элементов — int)</span>
<a id="__codelineno-205-4" name="__codelineno-205-4" href="#__codelineno-205-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
<a id="__codelineno-205-5" name="__codelineno-205-5" href="#__codelineno-205-5"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-205-6" name="__codelineno-205-6" href="#__codelineno-205-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-205-7" name="__codelineno-205-7" href="#__codelineno-205-7"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-205-8" name="__codelineno-205-8" href="#__codelineno-205-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-205-9" name="__codelineno-205-9" href="#__codelineno-205-9"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-205-10" name="__codelineno-205-10" href="#__codelineno-205-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-205-11" name="__codelineno-205-11" href="#__codelineno-205-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-205-12" name="__codelineno-205-12" href="#__codelineno-205-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-205-13" name="__codelineno-205-13" href="#__codelineno-205-13"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a id="__codelineno-205-14" name="__codelineno-205-14" href="#__codelineno-205-14"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
<a id="__codelineno-205-15" name="__codelineno-205-15" href="#__codelineno-205-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-205-16" name="__codelineno-205-16" href="#__codelineno-205-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
<a id="__codelineno-205-17" name="__codelineno-205-17" href="#__codelineno-205-17"></a><span class="p">}</span>
<a id="__codelineno-205-18" name="__codelineno-205-18" href="#__codelineno-205-18"></a>
<a id="__codelineno-205-19" name="__codelineno-205-19" href="#__codelineno-205-19"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-205-20" name="__codelineno-205-20" href="#__codelineno-205-20"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-205-21" name="__codelineno-205-21" href="#__codelineno-205-21"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-205-22" name="__codelineno-205-22" href="#__codelineno-205-22"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-205-23" name="__codelineno-205-23" href="#__codelineno-205-23"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-205-24" name="__codelineno-205-24" href="#__codelineno-205-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-205-25" name="__codelineno-205-25" href="#__codelineno-205-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-205-26" name="__codelineno-205-26" href="#__codelineno-205-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-205-27" name="__codelineno-205-27" href="#__codelineno-205-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
<a id="__codelineno-205-28" name="__codelineno-205-28" href="#__codelineno-205-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.kt</span><pre><span></span><code><a id="__codelineno-206-1" name="__codelineno-206-1" href="#__codelineno-206-1"></a><span class="cm">/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */</span>
<a id="__codelineno-206-2" name="__codelineno-206-2" href="#__codelineno-206-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-206-3" name="__codelineno-206-3" href="#__codelineno-206-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-206-4" name="__codelineno-206-4" href="#__codelineno-206-4"></a><span class="w"> </span><span class="c1">// Создать массив nums = { 1, 2, 3, ..., n }</span>
<a id="__codelineno-206-5" name="__codelineno-206-5" href="#__codelineno-206-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-206-6" name="__codelineno-206-6" href="#__codelineno-206-6"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-206-7" name="__codelineno-206-7" href="#__codelineno-206-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-206-8" name="__codelineno-206-8" href="#__codelineno-206-8"></a><span class="w"> </span><span class="c1">// Случайно перемешать элементы массива</span>
<a id="__codelineno-206-9" name="__codelineno-206-9" href="#__codelineno-206-9"></a><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">shuffle</span><span class="p">()</span>
<a id="__codelineno-206-10" name="__codelineno-206-10" href="#__codelineno-206-10"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-206-11" name="__codelineno-206-11" href="#__codelineno-206-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-206-12" name="__codelineno-206-12" href="#__codelineno-206-12"></a><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-206-13" name="__codelineno-206-13" href="#__codelineno-206-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-206-14" name="__codelineno-206-14" href="#__codelineno-206-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-206-15" name="__codelineno-206-15" href="#__codelineno-206-15"></a><span class="p">}</span>
<a id="__codelineno-206-16" name="__codelineno-206-16" href="#__codelineno-206-16"></a>
<a id="__codelineno-206-17" name="__codelineno-206-17" href="#__codelineno-206-17"></a><span class="cm">/* Найти индекс числа 1 в массиве nums */</span>
<a id="__codelineno-206-18" name="__codelineno-206-18" href="#__codelineno-206-18"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-206-19" name="__codelineno-206-19" href="#__codelineno-206-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-206-20" name="__codelineno-206-20" href="#__codelineno-206-20"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-206-21" name="__codelineno-206-21" href="#__codelineno-206-21"></a><span class="w"> </span><span class="c1">// Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-206-22" name="__codelineno-206-22" href="#__codelineno-206-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
<a id="__codelineno-206-23" name="__codelineno-206-23" href="#__codelineno-206-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
<a id="__codelineno-206-24" name="__codelineno-206-24" href="#__codelineno-206-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-206-25" name="__codelineno-206-25" href="#__codelineno-206-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
<a id="__codelineno-206-26" name="__codelineno-206-26" href="#__codelineno-206-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">worst_best_time_complexity.rb</span><pre><span></span><code><a id="__codelineno-207-1" name="__codelineno-207-1" href="#__codelineno-207-1"></a><span class="cm">=begin</span>
<a id="__codelineno-207-2" name="__codelineno-207-2" href="#__codelineno-207-2"></a><span class="cm">File: worst_best_time_complexity.rb</span>
<a id="__codelineno-207-3" name="__codelineno-207-3" href="#__codelineno-207-3"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-207-4" name="__codelineno-207-4" href="#__codelineno-207-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-207-5" name="__codelineno-207-5" href="#__codelineno-207-5"></a><span class="cm">=end</span>
<a id="__codelineno-207-6" name="__codelineno-207-6" href="#__codelineno-207-6"></a>
<a id="__codelineno-207-7" name="__codelineno-207-7" href="#__codelineno-207-7"></a><span class="c1"># ## Создать массив с элементами: 1, 2, ..., n в случайном порядке ###</span>
<a id="__codelineno-207-8" name="__codelineno-207-8" href="#__codelineno-207-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-207-9" name="__codelineno-207-9" href="#__codelineno-207-9"></a><span class="w"> </span><span class="c1"># Создать массив nums =: 1, 2, 3, ..., n</span>
<a id="__codelineno-207-10" name="__codelineno-207-10" href="#__codelineno-207-10"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-207-11" name="__codelineno-207-11" href="#__codelineno-207-11"></a><span class="w"> </span><span class="c1"># Случайно перемешать элементы массива</span>
<a id="__codelineno-207-12" name="__codelineno-207-12" href="#__codelineno-207-12"></a><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">shuffle!</span>
<a id="__codelineno-207-13" name="__codelineno-207-13" href="#__codelineno-207-13"></a><span class="k">end</span>
<a id="__codelineno-207-14" name="__codelineno-207-14" href="#__codelineno-207-14"></a>
<a id="__codelineno-207-15" name="__codelineno-207-15" href="#__codelineno-207-15"></a><span class="cm">=begin</span>
<a id="__codelineno-207-16" name="__codelineno-207-16" href="#__codelineno-207-16"></a><span class="cm">File: worst_best_time_complexity.rb</span>
<a id="__codelineno-207-17" name="__codelineno-207-17" href="#__codelineno-207-17"></a><span class="cm">Created Time: 2024-03-30</span>
<a id="__codelineno-207-18" name="__codelineno-207-18" href="#__codelineno-207-18"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-207-19" name="__codelineno-207-19" href="#__codelineno-207-19"></a><span class="cm">=end</span>
<a id="__codelineno-207-20" name="__codelineno-207-20" href="#__codelineno-207-20"></a>
<a id="__codelineno-207-21" name="__codelineno-207-21" href="#__codelineno-207-21"></a><span class="c1"># ## Создать массив с элементами: 1, 2, ..., n в случайном порядке ###</span>
<a id="__codelineno-207-22" name="__codelineno-207-22" href="#__codelineno-207-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<a id="__codelineno-207-23" name="__codelineno-207-23" href="#__codelineno-207-23"></a><span class="w"> </span><span class="c1"># Создать массив nums =: 1, 2, 3, ..., n</span>
<a id="__codelineno-207-24" name="__codelineno-207-24" href="#__codelineno-207-24"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-207-25" name="__codelineno-207-25" href="#__codelineno-207-25"></a><span class="w"> </span><span class="c1"># Случайно перемешать элементы массива</span>
<a id="__codelineno-207-26" name="__codelineno-207-26" href="#__codelineno-207-26"></a><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">shuffle!</span>
<a id="__codelineno-207-27" name="__codelineno-207-27" href="#__codelineno-207-27"></a><span class="k">end</span>
<a id="__codelineno-207-28" name="__codelineno-207-28" href="#__codelineno-207-28"></a>
<a id="__codelineno-207-29" name="__codelineno-207-29" href="#__codelineno-207-29"></a><span class="c1"># ## Найти индекс числа 1 в массиве nums ###</span>
<a id="__codelineno-207-30" name="__codelineno-207-30" href="#__codelineno-207-30"></a><span class="k">def</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-207-31" name="__codelineno-207-31" href="#__codelineno-207-31"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-207-32" name="__codelineno-207-32" href="#__codelineno-207-32"></a><span class="w"> </span><span class="c1"># Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)</span>
<a id="__codelineno-207-33" name="__codelineno-207-33" href="#__codelineno-207-33"></a><span class="w"> </span><span class="c1"># Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)</span>
<a id="__codelineno-207-34" name="__codelineno-207-34" href="#__codelineno-207-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-207-35" name="__codelineno-207-35" href="#__codelineno-207-35"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-207-36" name="__codelineno-207-36" href="#__codelineno-207-36"></a>
<a id="__codelineno-207-37" name="__codelineno-207-37" href="#__codelineno-207-37"></a><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-207-38" name="__codelineno-207-38" href="#__codelineno-207-38"></a><span class="k">end</span>
</code></pre></div>
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</details>
<p>Стоит отметить, что на практике мы редко используем лучшую временную сложность, поскольку обычно она достигается лишь с очень малой вероятностью и может вводить в заблуждение. <strong>Худшая временная сложность гораздо практичнее, потому что задает безопасную оценку эффективности</strong> и позволяет уверенно использовать алгоритм.</p>
<p>Из приведенного выше примера видно, что худшая и лучшая временные сложности возникают только при "особых распределениях данных"; вероятность таких случаев может быть низкой, и они не всегда реально отражают эффективность алгоритма. Напротив, <strong>средняя временная сложность способна показать эффективность алгоритма на случайных входных данных</strong> и обозначается символом <span class="arithmatex">\(\Theta\)</span> .</p>
<p>Для некоторых алгоритмов мы можем относительно просто вывести средний случай при случайном распределении данных. Например, в приведенном выше примере входной массив перемешан, а значит вероятность появления элемента <span class="arithmatex">\(1\)</span> на любом индексе одинакова; следовательно, среднее число итераций алгоритма равно половине длины массива, то есть <span class="arithmatex">\(n / 2\)</span> , а средняя временная сложность равна <span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span> .</p>
<p>Но для более сложных алгоритмов вычислить среднюю временную сложность часто непросто, потому что трудно проанализировать полное математическое ожидание на заданном распределении данных. В таких случаях мы обычно используем худшую временную сложность как критерий оценки эффективности алгоритма.</p>
<div class="admonition question">
<p class="admonition-title">Почему символ <span class="arithmatex">\(\Theta\)</span> встречается так редко?</p>
<p>Возможно, потому что символ <span class="arithmatex">\(O\)</span> звучит слишком привычно, и мы часто используем его для обозначения средней временной сложности. Но строго говоря, это некорректно. В этой книге и в других материалах, если встретится выражение вроде "средняя временная сложность <span class="arithmatex">\(O(n)\)</span>", просто понимай его как <span class="arithmatex">\(\Theta(n)\)</span> .</p>
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