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@@ -3918,7 +3918,7 @@
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<p>相较于直接统计算法运行时间，时间复杂度分析有哪些特点呢？</p>
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<ul>
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<li><strong>时间复杂度能够有效评估算法效率</strong>。例如，算法 <code>B</code> 的运行时间呈线性增长，在 <span class="arithmatex">\(n > 1\)</span> 时比算法 <code>A</code> 更慢，在 <span class="arithmatex">\(n > 1000000\)</span> 时比算法 <code>C</code> 更慢。事实上，只要输入数据大小 <span class="arithmatex">\(n\)</span> 足够大，复杂度为“常数阶”的算法一定优于“线性阶”的算法，这正是时间增长趋势所表达的含义。</li>
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<li><strong>时间复杂度的推算方法更简便</strong>。显然，运行平台和计算操作类型都与算法运行时间的增长趋势无关。因此在时间复杂度分析中，我们可以简单地将所有计算操作的执行时间视为相同的“单位时间”，从而将“计算操作的运行时间的统计”简化为“计算操作的数量的统计”，这样以来估算难度就大大降低了。</li>
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<li><strong>时间复杂度的推算方法更简便</strong>。显然，运行平台和计算操作类型都与算法运行时间的增长趋势无关。因此在时间复杂度分析中，我们可以简单地将所有计算操作的执行时间视为相同的“单位时间”，从而将“计算操作的运行时间的统计”简化为“计算操作的数量的统计”，这样一来估算难度就大大降低了。</li>
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<li><strong>时间复杂度也存在一定的局限性</strong>。例如，尽管算法 <code>A</code> 和 <code>C</code> 的时间复杂度相同，但实际运行时间差别很大。同样，尽管算法 <code>B</code> 的时间复杂度比 <code>C</code> 高，但在输入数据大小 <span class="arithmatex">\(n\)</span> 较小时，算法 <code>B</code> 明显优于算法 <code>C</code> 。在这些情况下，我们很难仅凭时间复杂度判断算法效率的高低。当然，尽管存在上述问题，复杂度分析仍然是评判算法效率最有效且常用的方法。</li>
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</ul>
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<h2 id="232">2.3.2 函数渐近上界<a class="headerlink" href="#232" title="Permanent link">¶</a></h2>
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@@ -5817,26 +5817,24 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
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<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">linearLogRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<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"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
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<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">1</span><span class="p">;</span>
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<a id="__codelineno-158-5" name="__codelineno-158-5" href="#__codelineno-158-5"></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>
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||||
<a id="__codelineno-158-6" name="__codelineno-158-6" href="#__codelineno-158-6"></a><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>
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<a id="__codelineno-158-7" name="__codelineno-158-7" href="#__codelineno-158-7"></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"><</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>
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<a id="__codelineno-158-8" name="__codelineno-158-8" href="#__codelineno-158-8"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
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<a id="__codelineno-158-9" name="__codelineno-158-9" href="#__codelineno-158-9"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-158-10" name="__codelineno-158-10" href="#__codelineno-158-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
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<a id="__codelineno-158-11" name="__codelineno-158-11" href="#__codelineno-158-11"></a><span class="p">}</span>
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<a id="__codelineno-158-5" name="__codelineno-158-5" href="#__codelineno-158-5"></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>
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<a id="__codelineno-158-6" name="__codelineno-158-6" href="#__codelineno-158-6"></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"><</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>
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<a id="__codelineno-158-7" name="__codelineno-158-7" href="#__codelineno-158-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
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<a id="__codelineno-158-8" name="__codelineno-158-8" href="#__codelineno-158-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-158-9" name="__codelineno-158-9" href="#__codelineno-158-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
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<a id="__codelineno-158-10" name="__codelineno-158-10" href="#__codelineno-158-10"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<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">/* 线性对数阶 */</span>
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<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">LinearLogRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<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"><=</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>
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<a id="__codelineno-159-4" name="__codelineno-159-4" href="#__codelineno-159-4"></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>
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||||
<a id="__codelineno-159-5" name="__codelineno-159-5" href="#__codelineno-159-5"></a><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-159-6" name="__codelineno-159-6" href="#__codelineno-159-6"></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"><</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>
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<a id="__codelineno-159-7" name="__codelineno-159-7" href="#__codelineno-159-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
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<a id="__codelineno-159-8" name="__codelineno-159-8" href="#__codelineno-159-8"></a><span class="w"> </span><span class="p">}</span>
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||||
<a id="__codelineno-159-9" name="__codelineno-159-9" href="#__codelineno-159-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
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<a id="__codelineno-159-10" name="__codelineno-159-10" href="#__codelineno-159-10"></a><span class="p">}</span>
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||||
<a id="__codelineno-159-4" name="__codelineno-159-4" href="#__codelineno-159-4"></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-159-5" name="__codelineno-159-5" href="#__codelineno-159-5"></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"><</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-159-6" name="__codelineno-159-6" href="#__codelineno-159-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||||
<a id="__codelineno-159-7" name="__codelineno-159-7" href="#__codelineno-159-7"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-159-8" name="__codelineno-159-8" href="#__codelineno-159-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
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<a id="__codelineno-159-9" name="__codelineno-159-9" href="#__codelineno-159-9"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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@@ -5845,13 +5843,12 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
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<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"><=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
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<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">1</span>
|
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<a id="__codelineno-160-5" name="__codelineno-160-5" href="#__codelineno-160-5"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-160-6" name="__codelineno-160-6" href="#__codelineno-160-6"></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>
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||||
<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></a><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>
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<a id="__codelineno-160-8" name="__codelineno-160-8" href="#__codelineno-160-8"></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="mf">0.0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</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>
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<a id="__codelineno-160-9" name="__codelineno-160-9" href="#__codelineno-160-9"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
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<a id="__codelineno-160-10" name="__codelineno-160-10" href="#__codelineno-160-10"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-160-11" name="__codelineno-160-11" href="#__codelineno-160-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
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<a id="__codelineno-160-12" name="__codelineno-160-12" href="#__codelineno-160-12"></a><span class="p">}</span>
|
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<a id="__codelineno-160-6" name="__codelineno-160-6" href="#__codelineno-160-6"></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>
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<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></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="mf">0.0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</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>
|
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<a id="__codelineno-160-8" name="__codelineno-160-8" href="#__codelineno-160-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
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<a id="__codelineno-160-9" name="__codelineno-160-9" href="#__codelineno-160-9"></a><span class="w"> </span><span class="p">}</span>
|
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<a id="__codelineno-160-10" name="__codelineno-160-10" href="#__codelineno-160-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
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<a id="__codelineno-160-11" name="__codelineno-160-11" href="#__codelineno-160-11"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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@@ -5910,13 +5907,12 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
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<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"><=</span><span class="w"> </span><span class="mf">1.0</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">1</span><span class="p">;</span>
|
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<a id="__codelineno-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a><span class="w"> </span><span class="p">}</span>
|
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<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></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="mf">2.0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span>
|
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<a id="__codelineno-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></a><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="mf">2.0</span><span class="p">);</span>
|
||||
<a id="__codelineno-165-8" name="__codelineno-165-8" href="#__codelineno-165-8"></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="w"> </span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-165-9" name="__codelineno-165-9" href="#__codelineno-165-9"></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">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-165-10" name="__codelineno-165-10" href="#__codelineno-165-10"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-165-11" name="__codelineno-165-11" href="#__codelineno-165-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
|
||||
<a id="__codelineno-165-12" name="__codelineno-165-12" href="#__codelineno-165-12"></a><span class="p">}</span>
|
||||
<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></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="mf">2.0</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="mf">2.0</span><span class="p">);</span>
|
||||
<a id="__codelineno-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></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="w"> </span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-165-8" name="__codelineno-165-8" href="#__codelineno-165-8"></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-165-9" name="__codelineno-165-9" href="#__codelineno-165-9"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-165-10" name="__codelineno-165-10" href="#__codelineno-165-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
|
||||
<a id="__codelineno-165-11" name="__codelineno-165-11" href="#__codelineno-165-11"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -5936,14 +5932,13 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="c1">// 线性对数阶</span>
|
||||
<a id="__codelineno-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</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"><=</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-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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>
|
||||
<a id="__codelineno-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></a><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-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</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-167-7" name="__codelineno-167-7" href="#__codelineno-167-7"></a><span class="w"> </span><span class="k">while</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="n">n</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><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-167-8" name="__codelineno-167-8" href="#__codelineno-167-8"></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-167-9" name="__codelineno-167-9" href="#__codelineno-167-9"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-167-10" name="__codelineno-167-10" href="#__codelineno-167-10"></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-167-11" name="__codelineno-167-11" href="#__codelineno-167-11"></a><span class="p">}</span>
|
||||
<a id="__codelineno-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</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-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></a><span class="w"> </span><span class="k">while</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="n">n</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><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-167-7" name="__codelineno-167-7" href="#__codelineno-167-7"></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-167-8" name="__codelineno-167-8" href="#__codelineno-167-8"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-167-9" name="__codelineno-167-9" href="#__codelineno-167-9"></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-167-10" name="__codelineno-167-10" href="#__codelineno-167-10"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -6227,25 +6222,22 @@ n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
|
||||
<a id="__codelineno-183-8" name="__codelineno-183-8" href="#__codelineno-183-8"></a>
|
||||
<a id="__codelineno-183-9" name="__codelineno-183-9" href="#__codelineno-183-9"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||||
<a id="__codelineno-183-10" name="__codelineno-183-10" href="#__codelineno-183-10"></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="m">0</span><span class="p">;</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="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-183-11" name="__codelineno-183-11" href="#__codelineno-183-11"></a><span class="w"> </span><span class="kt">var</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-183-12" name="__codelineno-183-12" href="#__codelineno-183-12"></a><span class="w"> </span><span class="kt">var</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">i</span><span class="p">];</span>
|
||||
<a id="__codelineno-183-13" name="__codelineno-183-13" href="#__codelineno-183-13"></a><span class="w"> </span><span class="kt">var</span><span class="w"> </span><span class="n">ran</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">index</span><span class="p">];</span>
|
||||
<a id="__codelineno-183-14" name="__codelineno-183-14" href="#__codelineno-183-14"></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">ran</span><span class="p">;</span>
|
||||
<a id="__codelineno-183-15" name="__codelineno-183-15" href="#__codelineno-183-15"></a><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="n">tmp</span><span class="p">;</span>
|
||||
<a id="__codelineno-183-16" name="__codelineno-183-16" href="#__codelineno-183-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-183-17" name="__codelineno-183-17" href="#__codelineno-183-17"></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-183-18" name="__codelineno-183-18" href="#__codelineno-183-18"></a><span class="p">}</span>
|
||||
<a id="__codelineno-183-19" name="__codelineno-183-19" href="#__codelineno-183-19"></a>
|
||||
<a id="__codelineno-183-20" name="__codelineno-183-20" href="#__codelineno-183-20"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||||
<a id="__codelineno-183-21" name="__codelineno-183-21" href="#__codelineno-183-21"></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-183-22" name="__codelineno-183-22" href="#__codelineno-183-22"></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"><</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-183-23" name="__codelineno-183-23" href="#__codelineno-183-23"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||||
<a id="__codelineno-183-24" name="__codelineno-183-24" href="#__codelineno-183-24"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||||
<a id="__codelineno-183-25" name="__codelineno-183-25" href="#__codelineno-183-25"></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>
|
||||
<a id="__codelineno-183-26" name="__codelineno-183-26" href="#__codelineno-183-26"></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-183-27" name="__codelineno-183-27" href="#__codelineno-183-27"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-183-28" name="__codelineno-183-28" href="#__codelineno-183-28"></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-183-29" name="__codelineno-183-29" href="#__codelineno-183-29"></a><span class="p">}</span>
|
||||
<a id="__codelineno-183-11" name="__codelineno-183-11" href="#__codelineno-183-11"></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-183-12" name="__codelineno-183-12" href="#__codelineno-183-12"></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-183-13" name="__codelineno-183-13" href="#__codelineno-183-13"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-183-14" name="__codelineno-183-14" href="#__codelineno-183-14"></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-183-15" name="__codelineno-183-15" href="#__codelineno-183-15"></a><span class="p">}</span>
|
||||
<a id="__codelineno-183-16" name="__codelineno-183-16" href="#__codelineno-183-16"></a>
|
||||
<a id="__codelineno-183-17" name="__codelineno-183-17" href="#__codelineno-183-17"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||||
<a id="__codelineno-183-18" name="__codelineno-183-18" href="#__codelineno-183-18"></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-183-19" name="__codelineno-183-19" href="#__codelineno-183-19"></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="m">0</span><span class="p">;</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="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-183-20" name="__codelineno-183-20" href="#__codelineno-183-20"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||||
<a id="__codelineno-183-21" name="__codelineno-183-21" href="#__codelineno-183-21"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||||
<a id="__codelineno-183-22" name="__codelineno-183-22" href="#__codelineno-183-22"></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="m">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-183-23" name="__codelineno-183-23" href="#__codelineno-183-23"></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-183-24" name="__codelineno-183-24" href="#__codelineno-183-24"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-183-25" name="__codelineno-183-25" href="#__codelineno-183-25"></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-183-26" name="__codelineno-183-26" href="#__codelineno-183-26"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
Reference in New Issue
Block a user