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chapter_computational_complexity/time_complexity/index.html
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@ -3258,7 +3258,7 @@ O((n - 1) \frac{n}{2}) = O(n^2)
<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kd">func</span> <span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 计数器</span>
<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a> <span class="c1">// 外循环：待排序元素数量为 n-1, n-2, ..., 1</span>
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">sequence</span><span class="p">(</span><span class="bp">first</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">next</span><span class="p">:</span> <span class="p">{</span> <span class="nv">$0</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="o">+</span> <span class="mi">1</span> <span class="p">?</span> <span class="nv">$0</span> <span class="o">-</span> <span class="mi">1</span> <span class="p">:</span> <span class="kc">nil</span> <span class="p">})</span> <span class="p">{</span>
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a> <span class="c1">// 内循环：冒泡操作</span>
<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o">&lt;</span> <span class="n">i</span> <span class="p">{</span>
<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></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> <span class="p">{</span>
@ -3870,7 +3870,7 @@ O((n - 1) \frac{n}{2}) = O(n^2)
<a id="__codelineno-138-4" name="__codelineno-138-4" href="#__codelineno-138-4"></a> <span class="k">return</span> <span class="mi">1</span>
<a id="__codelineno-138-5" name="__codelineno-138-5" href="#__codelineno-138-5"></a> <span class="p">}</span>
<a id="__codelineno-138-6" name="__codelineno-138-6" href="#__codelineno-138-6"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</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">linearLogRecur</span><span class="p">(</span><span class="n">n</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-138-7" name="__codelineno-138-7" href="#__codelineno-138-7"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="n">sequence</span><span class="p">(</span><span class="bp">first</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">next</span><span class="p">:</span> <span class="p">{</span> <span class="nv">$0</span> <span class="o">&lt;</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span> <span class="p">?</span> <span class="nv">$0</span> <span class="o">+</span> <span class="mi">1</span> <span class="p">:</span> <span class="kc">nil</span> <span class="p">})</span> <span class="p">{</span>
<a id="__codelineno-138-7" name="__codelineno-138-7" href="#__codelineno-138-7"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-138-8" name="__codelineno-138-8" href="#__codelineno-138-8"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-138-9" name="__codelineno-138-9" href="#__codelineno-138-9"></a> <span class="p">}</span>
<a id="__codelineno-138-10" name="__codelineno-138-10" href="#__codelineno-138-10"></a> <span class="k">return</span> <span class="bp">count</span>

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chapter_sorting/counting_sort/index.html
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@ -1875,7 +1875,26 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 计数排序 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// 简单实现，无法用于排序对象</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="kd">func</span> <span class="nf">countingSortNaive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="c1">// 1. 统计数组最大元素 m</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">nums</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="c1">// 2. 统计各数字的出现次数</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// counter[num] 代表 num 的出现次数</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kd">var</span> <span class="nv">counter</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="k">for</span> <span class="n">num</span> <span class="k">in</span> <span class="n">nums</span> <span class="p">{</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="p">}</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="c1">// 3. 遍历 counter ，将各元素填入原数组 nums</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="k">for</span> <span class="n">num</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">],</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="n">num</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="p">}</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="p">}</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -2080,7 +2099,35 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 计数排序 */</span>
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// 完整实现，可排序对象，并且是稳定排序</span>
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="kd">func</span> <span class="nf">countingSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a> <span class="c1">// 1. 统计数组最大元素 m</span>
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a> <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">nums</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a> <span class="c1">// 2. 统计各数字的出现次数</span>
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a> <span class="c1">// counter[num] 代表 num 的出现次数</span>
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a> <span class="kd">var</span> <span class="nv">counter</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a> <span class="k">for</span> <span class="n">num</span> <span class="k">in</span> <span class="n">nums</span> <span class="p">{</span>
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a> <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</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> <span class="c1">// 3. 求 counter 的前缀和，将“出现次数”转换为“尾索引”</span>
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a> <span class="c1">// 即 counter[num]-1 是 num 在 res 中最后一次出现的索引</span>
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">m</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a> <span class="n">counter</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a> <span class="p">}</span>
<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a> <span class="c1">// 4. 倒序遍历 nums ，将各元素填入结果数组 res</span>
<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a> <span class="c1">// 初始化数组 res 用于记录结果</span>
<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a> <span class="kd">var</span> <span class="nv">res</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">through</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a> <span class="kd">let</span> <span class="nv">num</span> <span class="p">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a> <span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="n">num</span> <span class="c1">// 将 num 放置到对应索引处</span>
<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a> <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span> <span class="c1">// 令前缀和自减 1 ，得到下次放置 num 的索引</span>
<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a> <span class="p">}</span>
<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a> <span class="c1">// 使用结果数组 res 覆盖原数组 nums</span>
<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a> <span class="p">}</span>
<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="p">}</span>
</code></pre></div>
</div>
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