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@@ -62,17 +62,15 @@
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@@ -3670,12 +3668,12 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
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<div class="highlight"><span class="filename">radix_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<div class="highlight"><span class="filename">radix_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;获取元素 num 的第 k 位，其中 exp = 10^(k-1)&quot;&quot;&quot;</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="k">return</span> <span class="p">(</span><span class="n">num</span> <span class="o">//</span> <span class="n">exp</span><span class="p">)</span> <span class="o">%</span> <span class="mi">10</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="k">def</span> <span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;计数排序（根据 nums 第 k 位排序）&quot;&quot;&quot;</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="c1"># 十进制的位范围为 0~9 ，因此需要长度为 10 的桶数组</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10</span>
@@ -3698,7 +3696,7 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="k">def</span> <span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="k">def</span><span class="w"> </span><span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;基数排序&quot;&quot;&quot;</span>
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a> <span class="c1"># 获取数组的最大元素，用于判断最大位数</span>
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a> <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
@@ -3817,33 +3815,33 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
<div class="highlight"><span class="filename">radix_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">10</span><span class="p">;</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 计数排序（根据 nums 第 k 位排序） */</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="k">void</span><span class="w"> </span><span class="nf">CountingSortDigit</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="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 十进制的位范围为 0~9 ，因此需要长度为 10 的桶数组</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="m">10</span><span class="p">];</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</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>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 统计 0~9 各数字的出现次数</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="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-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="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-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Digit</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">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// 获取 nums[i] 第 k 位，记为 d</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 统计数字 d 的出现次数</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="c1">// 求前缀和，将“出现个数”转换为“数组索引”</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">10</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-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="n">counter</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">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</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-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="n">counter</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">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="c1">// 倒序遍历，根据桶内统计结果，将各元素填入 res</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Digit</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">exp</span><span class="p">);</span>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 获取 d 在数组中的索引 j</span>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 获取 d 在数组中的索引 j</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将当前元素填入索引 j</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 d 的数量减 1</span>
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w"> </span><span class="c1">// 使用结果覆盖原数组 nums</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></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">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="p">}</span>
@@ -3856,7 +3854,7 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w"> </span><span class="c1">// 按照从低位到高位的顺序遍历</span>
<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></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">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></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">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w"> </span><span class="c1">// 对数组元素的第 k 位执行计数排序</span>
<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w"> </span><span class="c1">// k = 1 -&gt; exp = 1</span>
<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="w"> </span><span class="c1">// k = 2 -&gt; exp = 10</span>
@@ -3923,55 +3921,55 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">radix_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">exp</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-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="c1">// 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="p">(</span><span class="n">num</span> <span class="o">/</span> <span class="n">exp</span><span class="p">)</span> <span class="o">%</span> <span class="mi">10</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">}</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="cm">/* 计数排序（根据 nums 第 k 位排序） */</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="kd">func</span> <span class="nf">countingSortDigit</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="n">exp</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="c1">// 十进制的位范围为 0~9 ，因此需要长度为 10 的桶数组</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></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="mi">10</span><span class="p">)</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <span class="c1">// 统计 0~9 各数字的出现次数</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">nums</span><span class="p">.</span><span class="bp">indices</span> <span class="p">{</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="kd">let</span> <span class="nv">d</span> <span class="p">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">num</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="n">exp</span><span class="p">:</span> <span class="n">exp</span><span class="p">)</span> <span class="c1">// 获取 nums[i] 第 k 位，记为 d</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a> <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span> <span class="c1">// 统计数字 d 的出现次数</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a> <span class="p">}</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a> <span class="c1">// 求前缀和，将“出现个数”转换为“数组索引”</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="mi">1</span> <span class="p">..</span><span class="o">&lt;</span> <span class="mi">10</span> <span class="p">{</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="n">counter</span><span class="p">[</span><span class="n">i</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="o">-</span> <span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a> <span class="p">}</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a> <span class="c1">// 倒序遍历，根据桶内统计结果，将各元素填入 res</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></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-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="n">reversed</span><span class="p">()</span> <span class="p">{</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a> <span class="kd">let</span> <span class="nv">d</span> <span class="p">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">num</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="n">exp</span><span class="p">:</span> <span class="n">exp</span><span class="p">)</span>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a> <span class="kd">let</span> <span class="nv">j</span> <span class="p">=</span> <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1">// 获取 d 在数组中的索引 j</span>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a> <span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</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="c1">// 将当前元素填入索引 j</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a> <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span> <span class="c1">// 将 d 的数量减 1</span>
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a> <span class="p">}</span>
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a> <span class="c1">// 使用结果覆盖原数组 nums</span>
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">nums</span><span class="p">.</span><span class="bp">indices</span> <span class="p">{</span>
<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></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-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a> <span class="p">}</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="kd">func</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="c1">// 十进制的位范围为 0~9 ，因此需要长度为 10 的桶数组</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="c1">// 统计 0~9 各数字的出现次数</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">num</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><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="c1">// 获取 nums[i] 第 k 位，记为 d</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 统计数字 d 的出现次数</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="c1">// 求前缀和，将“出现个数”转换为“数组索引”</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="n">counter</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">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w"> </span><span class="c1">// 倒序遍历，根据桶内统计结果，将各元素填入 res</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">num</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><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 获取 d 在数组中的索引 j</span>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="c1">// 将当前元素填入索引 j</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 将 d 的数量减 1</span>
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w"> </span><span class="c1">// 使用结果覆盖原数组 nums</span>
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></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="p">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="p">}</span>
<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a>
<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="cm">/* 基数排序 */</span>
<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="kd">func</span> <span class="nf">radixSort</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-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a> <span class="c1">// 获取数组的最大元素，用于判断最大位数</span>
<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a> <span class="kd">var</span> <span class="nv">m</span> <span class="p">=</span> <span class="nb">Int</span><span class="p">.</span><span class="bp">min</span>
<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></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-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a> <span class="k">if</span> <span class="n">num</span> <span class="o">&gt;</span> <span class="n">m</span> <span class="p">{</span>
<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a> <span class="n">m</span> <span class="p">=</span> <span class="n">num</span>
<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a> <span class="p">}</span>
<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a> <span class="p">}</span>
<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a> <span class="c1">// 按照从低位到高位的顺序遍历</span>
<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a> <span class="k">for</span> <span class="n">exp</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">1</span><span class="p">,</span> <span class="n">next</span><span class="p">:</span> <span class="p">{</span> <span class="n">m</span> <span class="o">&gt;=</span> <span class="p">(</span><span class="nv">$0</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span> <span class="p">?</span> <span class="nv">$0</span> <span class="o">*</span> <span class="mi">10</span> <span class="p">:</span> <span class="kc">nil</span> <span class="p">})</span> <span class="p">{</span>
<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a> <span class="c1">// 对数组元素的第 k 位执行计数排序</span>
<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a> <span class="c1">// k = 1 -&gt; exp = 1</span>
<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a> <span class="c1">// k = 2 -&gt; exp = 10</span>
<a id="__codelineno-5-48" name="__codelineno-5-48" href="#__codelineno-5-48"></a> <span class="c1">// 即 exp = 10^(k-1)</span>
<a id="__codelineno-5-49" name="__codelineno-5-49" href="#__codelineno-5-49"></a> <span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span> <span class="n">exp</span><span class="p">:</span> <span class="n">exp</span><span class="p">)</span>
<a id="__codelineno-5-50" name="__codelineno-5-50" href="#__codelineno-5-50"></a> <span class="p">}</span>
<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="kd">func</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w"> </span><span class="c1">// 获取数组的最大元素，用于判断最大位数</span>
<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Int</span><span class="p">.</span><span class="bp">min</span>
<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w"> </span><span class="c1">// 按照从低位到高位的顺序遍历</span>
<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">sequence</span><span class="p">(</span><span class="bp">first</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="p">(</span><span class="nv">$0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">})</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w"> </span><span class="c1">// 对数组元素的第 k 位执行计数排序</span>
<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w"> </span><span class="c1">// k = 1 -&gt; exp = 1</span>
<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="w"> </span><span class="c1">// k = 2 -&gt; exp = 10</span>
<a id="__codelineno-5-48" name="__codelineno-5-48" href="#__codelineno-5-48"></a><span class="w"> </span><span class="c1">// 即 exp = 10^(k-1)</span>
<a id="__codelineno-5-49" name="__codelineno-5-49" href="#__codelineno-5-49"></a><span class="w"> </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
<a id="__codelineno-5-50" name="__codelineno-5-50" href="#__codelineno-5-50"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-51" name="__codelineno-5-51" href="#__codelineno-5-51"></a><span class="p">}</span>
</code></pre></div>
</div>
@@ -4126,13 +4124,13 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">radix_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">digit</span><span class="p">(</span><span class="n">num</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">usize</span> <span class="p">{</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="c1">// 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">((</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">;</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">}</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="cm">/* 计数排序（根据 nums 第 k 位排序） */</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="k">fn</span> <span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="k">fn</span><span class="w"> </span><span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="c1">// 十进制的位范围为 0~9 ，因此需要长度为 10 的桶数组</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></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">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10</span><span class="p">];</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</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">len</span><span class="p">();</span>
@@ -4158,7 +4156,7 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="p">}</span>
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a>
<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="cm">/* 基数排序 */</span>
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="k">fn</span> <span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="k">fn</span><span class="w"> </span><span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w"> </span><span class="c1">// 获取数组的最大元素，用于判断最大位数</span>
<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">.</span><span class="n">into_iter</span><span class="p">().</span><span class="n">max</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w"> </span><span class="c1">// 按照从低位到高位的顺序遍历</span>
@@ -4659,5 +4657,7 @@ aria-label="页脚"
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