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@@ -3323,7 +3323,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
<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">/* 常数阶 */</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">10</span><span class="n">_0000</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>
@@ -4141,7 +4141,7 @@ 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!
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></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-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></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-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></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">// 计数器</span>
<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</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="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-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
@@ -5068,7 +5068,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
<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="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-189-4" name="__codelineno-189-4" href="#__codelineno-189-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-189-5" name="__codelineno-189-5" href="#__codelineno-189-5"></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-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="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="na">toInt</span><span class="p">())</span><span class="w"> </span><span class="p">{</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="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-189-7" name="__codelineno-189-7" href="#__codelineno-189-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</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="n">count</span>
@@ -5637,27 +5637,26 @@ n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
<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">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<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>
<a id="__codelineno-217-7" name="__codelineno-217-7" href="#__codelineno-217-7"></a><span class="w"> </span><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="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>
<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>
<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>
<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>
<a id="__codelineno-217-11" name="__codelineno-217-11" href="#__codelineno-217-11"></a><span class="w"> </span><span class="c1">// Integer[] -&gt; int[]</span>
<a id="__codelineno-217-12" name="__codelineno-217-12" href="#__codelineno-217-12"></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-217-13" name="__codelineno-217-13" href="#__codelineno-217-13"></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="n">n</span><span class="p">)</span><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="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>
<a id="__codelineno-217-15" name="__codelineno-217-15" href="#__codelineno-217-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-217-16" name="__codelineno-217-16" href="#__codelineno-217-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-217-17" name="__codelineno-217-17" href="#__codelineno-217-17"></a><span class="p">}</span>
<a id="__codelineno-217-18" name="__codelineno-217-18" href="#__codelineno-217-18"></a>
<a id="__codelineno-217-19" name="__codelineno-217-19" href="#__codelineno-217-19"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
<a id="__codelineno-217-20" name="__codelineno-217-20" href="#__codelineno-217-20"></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-217-21" name="__codelineno-217-21" href="#__codelineno-217-21"></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-217-22" name="__codelineno-217-22" href="#__codelineno-217-22"></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-217-23" name="__codelineno-217-23" href="#__codelineno-217-23"></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-217-24" name="__codelineno-217-24" href="#__codelineno-217-24"></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="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-217-25" name="__codelineno-217-25" href="#__codelineno-217-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
<a id="__codelineno-217-26" name="__codelineno-217-26" href="#__codelineno-217-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-217-27" name="__codelineno-217-27" href="#__codelineno-217-27"></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-217-28" name="__codelineno-217-28" href="#__codelineno-217-28"></a><span class="p">}</span>
<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">&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-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">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<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>
<a id="__codelineno-217-14" name="__codelineno-217-14" href="#__codelineno-217-14"></a><span class="w"> </span><span class="p">}</span>
<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>
<a id="__codelineno-217-16" name="__codelineno-217-16" href="#__codelineno-217-16"></a><span class="p">}</span>
<a id="__codelineno-217-17" name="__codelineno-217-17" href="#__codelineno-217-17"></a>
<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>
<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">&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-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>
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<div class="tabbed-block">