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@ -1860,19 +1860,19 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \mod d
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<div class="highlight"><span class="filename">radix_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></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>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></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-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></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-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></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-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></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-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a> <span class="c1"># 十进制的位范围为 0~9 ，因此需要长度为 10 的桶</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></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>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="c1"># 统计 0~9 各数字的出现次数</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></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-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a> <span class="n">d</span> <span class="o">=</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="n">exp</span><span class="p">)</span> <span class="c1"># 获取 nums[i] 第 k 位，记为 d</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></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-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></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-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="c1"># 求前缀和，将“出现个数”转换为“数组索引”</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></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="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">):</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></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>
@ -1881,14 +1881,14 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \mod d
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></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="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="n">d</span> <span class="o">=</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="n">exp</span><span class="p">)</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="n">j</span> <span class="o">=</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-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</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-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></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-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</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-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></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-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a> <span class="c1"># 使用结果覆盖原数组 nums</span>
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></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-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></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-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a>
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></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> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 基数排序 &quot;&quot;&quot;</span>
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;基数排序&quot;&quot;&quot;</span>
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></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-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></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>
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a> <span class="c1"># 按照从低位到高位的顺序遍历</span>