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chapter_sorting/radix_sort/index.html

@@ -3392,7 +3392,7 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
 \]</div>
 <p>其中 <span class="arithmatex">\(\lfloor a \rfloor\)</span> 表示对浮点数 <span class="arithmatex">\(a\)</span> 向下取整，而 <span class="arithmatex">\(\bmod \space d\)</span> 表示对 <span class="arithmatex">\(d\)</span> 取余。对于学号数据，<span class="arithmatex">\(d = 10\)</span> 且 <span class="arithmatex">\(k \in [1, 8]\)</span> 。</p>
 <p>此外，我们需要小幅改动计数排序代码，使之可以根据数字的第 <span class="arithmatex">\(k\)</span> 位进行排序。</p>
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 <div class="highlight"><span class="filename">radix_sort.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */</span>
@@ -3976,6 +3976,54 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
 <a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="p">}</span>
 </code></pre></div>
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+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.rs</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></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-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></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-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></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-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 计数排序（根据 nums 第 k 位排序） */</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></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-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></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</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></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-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></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>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="c1">// 统计 0~9 各数字的出现次数</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></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">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="kd">let</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-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></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="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">// 统计数字 d 的出现次数</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></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-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></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="o">..</span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></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-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></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-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></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">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></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="p">(</span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">        </span><span class="kd">let</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-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">        </span><span class="kd">let</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-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></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-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></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="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">// 将 d 的数量减 1</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="c1">// 使用结果覆盖原数组 nums</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></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">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></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-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="p">}</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="cm">/* 基数排序 */</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></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-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></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-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></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-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></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-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></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">exp</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-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">    </span><span class="k">while</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="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="w">        </span><span class="n">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><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>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="p">}</span>
+</code></pre></div>
+</div>
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