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@@ -3540,11 +3540,10 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 线性阶 */</span>
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<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></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>
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<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></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>
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<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
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<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></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"><</span><span class="n">n</span><span class="p">)</span>
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<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
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<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
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<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="p">}</span>
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<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></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"><</span><span class="n">n</span><span class="p">)</span>
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<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
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<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
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||||
<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></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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@@ -4205,13 +4204,15 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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<a id="__codelineno-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></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"><</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></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">></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>
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<a id="__codelineno-119-9" name="__codelineno-119-9" href="#__codelineno-119-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
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<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></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><span class="p">.</span><span class="na">also</span><span class="w"> </span><span class="p">{</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="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="w"> </span><span class="p">}</span>
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<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
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<a id="__codelineno-119-12" name="__codelineno-119-12" href="#__codelineno-119-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-119-13" name="__codelineno-119-13" href="#__codelineno-119-13"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-119-14" name="__codelineno-119-14" href="#__codelineno-119-14"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-119-15" name="__codelineno-119-15" href="#__codelineno-119-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
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<a id="__codelineno-119-16" name="__codelineno-119-16" href="#__codelineno-119-16"></a><span class="p">}</span>
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<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></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>
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<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></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>
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<a id="__codelineno-119-12" name="__codelineno-119-12" href="#__codelineno-119-12"></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>
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||||
<a id="__codelineno-119-13" name="__codelineno-119-13" href="#__codelineno-119-13"></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">// 元素交换包含 3 个单元操作</span>
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||||
<a id="__codelineno-119-14" name="__codelineno-119-14" href="#__codelineno-119-14"></a><span class="w"> </span><span class="p">}</span>
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||||
<a id="__codelineno-119-15" name="__codelineno-119-15" href="#__codelineno-119-15"></a><span class="w"> </span><span class="p">}</span>
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||||
<a id="__codelineno-119-16" name="__codelineno-119-16" href="#__codelineno-119-16"></a><span class="w"> </span><span class="p">}</span>
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||||
<a id="__codelineno-119-17" name="__codelineno-119-17" href="#__codelineno-119-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
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||||
<a id="__codelineno-119-18" name="__codelineno-119-18" href="#__codelineno-119-18"></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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@@ -4455,8 +4456,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
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<a id="__codelineno-133-2" name="__codelineno-133-2" href="#__codelineno-133-2"></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>
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<a id="__codelineno-133-3" name="__codelineno-133-3" href="#__codelineno-133-3"></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>
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<a id="__codelineno-133-4" name="__codelineno-133-4" href="#__codelineno-133-4"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
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<a id="__codelineno-133-5" name="__codelineno-133-5" href="#__codelineno-133-5"></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>
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<a id="__codelineno-133-4" name="__codelineno-133-4" href="#__codelineno-133-4"></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>
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<a id="__codelineno-133-5" name="__codelineno-133-5" href="#__codelineno-133-5"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
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<a id="__codelineno-133-6" name="__codelineno-133-6" href="#__codelineno-133-6"></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"><</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-133-7" name="__codelineno-133-7" href="#__codelineno-133-7"></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"><</span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-133-8" name="__codelineno-133-8" href="#__codelineno-133-8"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
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@@ -5694,26 +5695,25 @@ n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
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<a id="__codelineno-217-5" name="__codelineno-217-5" href="#__codelineno-217-5"></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"><</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-217-6" name="__codelineno-217-6" href="#__codelineno-217-6"></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>
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<a id="__codelineno-217-7" name="__codelineno-217-7" href="#__codelineno-217-7"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-217-8" name="__codelineno-217-8" href="#__codelineno-217-8"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">mutableList</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">toMutableList</span><span class="p">()</span>
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<a id="__codelineno-217-9" name="__codelineno-217-9" href="#__codelineno-217-9"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
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<a id="__codelineno-217-10" name="__codelineno-217-10" href="#__codelineno-217-10"></a><span class="w"> </span><span class="n">mutableList</span><span class="p">.</span><span class="na">shuffle</span><span class="p">()</span>
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<a id="__codelineno-217-11" name="__codelineno-217-11" href="#__codelineno-217-11"></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"><</span><span class="kt">Int</span><span class="o">></span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
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<a id="__codelineno-217-12" name="__codelineno-217-12" href="#__codelineno-217-12"></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"><</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-217-13" name="__codelineno-217-13" href="#__codelineno-217-13"></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">mutableList</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
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<a id="__codelineno-217-14" name="__codelineno-217-14" href="#__codelineno-217-14"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-217-15" name="__codelineno-217-15" href="#__codelineno-217-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
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||||
<a id="__codelineno-217-16" name="__codelineno-217-16" href="#__codelineno-217-16"></a><span class="p">}</span>
|
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<a id="__codelineno-217-17" name="__codelineno-217-17" href="#__codelineno-217-17"></a>
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<a id="__codelineno-217-18" name="__codelineno-217-18" href="#__codelineno-217-18"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
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<a id="__codelineno-217-19" name="__codelineno-217-19" href="#__codelineno-217-19"></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"><</span><span class="kt">Int?</span><span class="o">></span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
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||||
<a id="__codelineno-217-20" name="__codelineno-217-20" href="#__codelineno-217-20"></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-217-21" name="__codelineno-217-21" href="#__codelineno-217-21"></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-217-22" name="__codelineno-217-22" href="#__codelineno-217-22"></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-217-23" name="__codelineno-217-23" href="#__codelineno-217-23"></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="m">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-217-24" name="__codelineno-217-24" href="#__codelineno-217-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
|
||||
<a id="__codelineno-217-25" name="__codelineno-217-25" href="#__codelineno-217-25"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-217-26" name="__codelineno-217-26" href="#__codelineno-217-26"></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-217-27" name="__codelineno-217-27" href="#__codelineno-217-27"></a><span class="p">}</span>
|
||||
<a id="__codelineno-217-8" name="__codelineno-217-8" href="#__codelineno-217-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||||
<a id="__codelineno-217-9" name="__codelineno-217-9" href="#__codelineno-217-9"></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-217-10" name="__codelineno-217-10" href="#__codelineno-217-10"></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"><</span><span class="kt">Int</span><span class="o">></span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-217-11" name="__codelineno-217-11" href="#__codelineno-217-11"></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"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-217-12" name="__codelineno-217-12" href="#__codelineno-217-12"></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-217-13" name="__codelineno-217-13" href="#__codelineno-217-13"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-217-14" name="__codelineno-217-14" href="#__codelineno-217-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-217-15" name="__codelineno-217-15" href="#__codelineno-217-15"></a><span class="p">}</span>
|
||||
<a id="__codelineno-217-16" name="__codelineno-217-16" href="#__codelineno-217-16"></a>
|
||||
<a id="__codelineno-217-17" name="__codelineno-217-17" href="#__codelineno-217-17"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||||
<a id="__codelineno-217-18" name="__codelineno-217-18" href="#__codelineno-217-18"></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"><</span><span class="kt">Int?</span><span class="o">></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-217-19" name="__codelineno-217-19" href="#__codelineno-217-19"></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-217-20" name="__codelineno-217-20" href="#__codelineno-217-20"></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-217-21" name="__codelineno-217-21" href="#__codelineno-217-21"></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-217-22" name="__codelineno-217-22" href="#__codelineno-217-22"></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-217-23" name="__codelineno-217-23" href="#__codelineno-217-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
|
||||
<a id="__codelineno-217-24" name="__codelineno-217-24" href="#__codelineno-217-24"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-217-25" name="__codelineno-217-25" href="#__codelineno-217-25"></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-217-26" name="__codelineno-217-26" href="#__codelineno-217-26"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
Reference in New Issue
Block a user