deploy

chapter_graph/graph_traversal/index.html

@@ -2018,7 +2018,36 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 广度优先遍历 BFS */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</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="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="c1">// 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">startVet</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 队列用于实现 BFS</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// 以顶点 vet 为起点，循环直至访问完所有顶点</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">que</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 队首顶点出队</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">               </span><span class="c1">// 记录访问顶点</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">        </span><span class="p">{</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">            </span><span class="p">{</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">          </span><span class="c1">// 跳过已被访问过的顶点</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 只入队未访问的顶点</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 标记该顶点已被访问</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="c1">// 返回顶点遍历序列</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -2274,9 +2303,34 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 深度优先遍历 DFS 辅助函数 */</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">{</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">     </span><span class="c1">// 记录访问顶点</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 标记该顶点已被访问</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// 遍历该顶点的所有邻接顶点</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="p">{</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳过已被访问过的顶点                             </span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="c1">// 递归访问邻接顶点</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="cm">/* 深度优先遍历 DFS */</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="c1">// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="p">{</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</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="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="c1">// 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">

chapter_sorting/bucket_sort/index.html

@@ -1950,7 +1950,40 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bucket_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 桶排序 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="kt">float</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">{</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// 初始化 k = n/2 个桶，预期向每个桶分配 2 个元素</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</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="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></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">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="p">());</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// 1. 将数组元素分配到各个桶中</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">float</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="p">)</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="c1">// 输入数据范围 [0, 1)，使用 num * k 映射到索引范围 [0, k-1]</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </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="p">(</span><span class="kt">int</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">k</span><span class="p">;</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="c1">// 将 num 添加进桶 i</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">Add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="c1">// 2. 对各个桶执行排序</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">        </span><span class="c1">// 使用内置排序函数，也可以替换成其他排序算法</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="n">Sort</span><span class="p">();</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="c1">// 3. 遍历桶合并结果</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></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="m">0</span><span class="p">;</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">float</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">bucket</span><span class="p">)</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">        </span><span class="p">{</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">]</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-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">

chapter_sorting/counting_sort/index.html

@@ -1934,7 +1934,33 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 计数排序 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// 简单实现，无法用于排序对象</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="k">void</span><span class="w"> </span><span class="nf">countingSortNaive</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>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="c1">// 1. 统计数组最大元素 m</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">)</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// 2. 统计各数字的出现次数</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// counter[num] 代表 num 的出现次数</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></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="n">m</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-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">)</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </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="p">;</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// 3. 遍历 counter ，将各元素填入原数组 nums</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </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>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></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">num</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">num</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="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">];</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">        </span><span class="p">{</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></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">num</span><span class="p">;</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -2226,7 +2252,45 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 计数排序 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// 完整实现，可排序对象，并且是稳定排序</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="k">void</span><span class="w"> </span><span class="nf">countingSort</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>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="c1">// 1. 统计数组最大元素 m</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">)</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="c1">// 2. 统计各数字的出现次数</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="c1">// counter[num] 代表 num 的出现次数</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></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="n">m</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-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">)</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </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="p">;</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><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-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><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-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></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">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><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><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="p">];</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="c1">// 4. 倒序遍历 nums ，将各元素填入结果数组 res</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="c1">// 初始化数组 res 用于记录结果</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></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-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></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-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></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>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</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>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">        </span><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="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="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 num 放置到对应索引处</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">        </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="p">;</span><span class="w"> </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-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="c1">// 使用结果数组 res 覆盖原数组 nums</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></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>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></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-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">

chapter_sorting/radix_sort/index.html

@@ -2077,11 +2077,65 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \mod d
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></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>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">{</span>
-<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></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-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></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-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="p">}</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="cm">/* 计数排序（根据 nums 第 k 位排序） */</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></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>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></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-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></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-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></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-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="c1">// 统计 0~9 各数字的出现次数</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></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>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></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-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></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-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></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-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></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>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></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-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></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-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></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-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></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>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></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-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></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-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></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-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></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-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">    </span><span class="c1">// 使用结果覆盖原数组 nums</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></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>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></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-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="p">}</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a><span class="cm">/* 基数排序 */</span>
+<a id="__codelineno-7-42" name="__codelineno-7-42" href="#__codelineno-7-42"></a><span class="k">void</span><span class="w"> </span><span class="nf">radixSort</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>
+<a id="__codelineno-7-43" name="__codelineno-7-43" href="#__codelineno-7-43"></a><span class="p">{</span>
+<a id="__codelineno-7-44" name="__codelineno-7-44" href="#__codelineno-7-44"></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-7-45" name="__codelineno-7-45" href="#__codelineno-7-45"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">int</span><span class="p">.</span><span class="n">MinValue</span><span class="p">;</span>
+<a id="__codelineno-7-46" name="__codelineno-7-46" href="#__codelineno-7-46"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">)</span>
+<a id="__codelineno-7-47" name="__codelineno-7-47" href="#__codelineno-7-47"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-48" name="__codelineno-7-48" href="#__codelineno-7-48"></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-7-49" name="__codelineno-7-49" href="#__codelineno-7-49"></a><span class="w">    </span><span class="p">}</span><span class="w">               </span>
+<a id="__codelineno-7-50" name="__codelineno-7-50" href="#__codelineno-7-50"></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-7-51" name="__codelineno-7-51" href="#__codelineno-7-51"></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>
+<a id="__codelineno-7-52" name="__codelineno-7-52" href="#__codelineno-7-52"></a><span class="w">    </span><span class="p">{</span>
+<a id="__codelineno-7-53" name="__codelineno-7-53" href="#__codelineno-7-53"></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-7-54" name="__codelineno-7-54" href="#__codelineno-7-54"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-7-55" name="__codelineno-7-55" href="#__codelineno-7-55"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-7-56" name="__codelineno-7-56" href="#__codelineno-7-56"></a><span class="w">        </span><span class="c1">// 即 exp = 10^(k-1)</span>
+<a id="__codelineno-7-57" name="__codelineno-7-57" href="#__codelineno-7-57"></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="n">exp</span><span class="p">);</span>
+<a id="__codelineno-7-58" name="__codelineno-7-58" href="#__codelineno-7-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-59" name="__codelineno-7-59" href="#__codelineno-7-59"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">