deploy

2026-04-14 02:10:37 +08:00 · 2024-04-28 22:36:06 +08:00
parent 7803a73a99
commit b1bd0c8f8d
43 changed files with 990 additions and 430 deletions
--- a/chapter_graph/graph_traversal/index.html
+++ b/chapter_graph/graph_traversal/index.html
@@ -3774,7 +3774,11 @@
 <li>在循环的每轮迭代中，弹出队首顶点并记录访问，然后将该顶点的所有邻接顶点加入到队列尾部。</li>
 <li>循环步骤 <code>2.</code> ，直到所有顶点被访问完毕后结束。</li>
 </ol>
-<p>为了防止重复遍历顶点，我们需要借助一个哈希表 <code>visited</code> 来记录哪些节点已被访问。</p>
+<p>为了防止重复遍历顶点，我们需要借助一个哈希集合 <code>visited</code> 来记录哪些节点已被访问。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>哈希集合可以看作一个只存储 <code>key</code> 而不存储 <code>value</code> 的哈希表，它可以在 <span class="arithmatex">\(O(1)\)</span> 时间复杂度下进行 <code>key</code> 的增删查改操作。根据 <code>key</code> 的唯一性，哈希集合通常用于数据去重等场景。</p>
+</div>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -3783,7 +3787,7 @@
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></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-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 顶点遍历序列</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 队列用于实现 BFS</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">que</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
@@ -3807,7 +3811,7 @@
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </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="o">&amp;</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="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></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-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </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="p">{</span><span class="n">startVet</span><span class="p">};</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 队列用于实现 BFS</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="n">queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">que</span><span class="p">;</span>
@@ -3836,7 +3840,7 @@
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></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="nf">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><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></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">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">Set</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;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 队列用于实现 BFS</span>
@@ -3865,7 +3869,7 @@
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></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><span class="w"> </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="c1">// 顶点遍历序列</span>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></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="p">[];</span>
-<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></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-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></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="p">[</span><span class="n">startVet</span><span class="p">];</span>
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// 队列用于实现 BFS</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></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="p">();</span>
@@ -3894,7 +3898,7 @@
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></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-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="nx">visited</span><span class="p">[</span><span class="nx">startVet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 队列用于实现 BFS, 使用切片模拟队列</span>
@@ -3928,7 +3932,7 @@
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">func</span> <span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">startVet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">{</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>    <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="c1">// 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="kd">var</span> <span class="nv">visited</span><span class="p">:</span> <span class="n">Set</span><span class="p">&lt;</span><span class="n">Vertex</span><span class="p">&gt;</span> <span class="p">=</span> <span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>    <span class="c1">// 队列用于实现 BFS</span>
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>    <span class="kd">var</span> <span class="nv">que</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
@@ -3956,7 +3960,7 @@
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
-<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></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-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// 队列用于实现 BFS</span>
@@ -3985,7 +3989,7 @@
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><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">// 顶点遍历序列</span>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="c1">// 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o">&lt;</span><span class="nx">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</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="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</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>
@@ -4014,7 +4018,7 @@
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><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-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></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="p">[];</span>
-<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></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-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">Set</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="p">{};</span>
 <a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></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">startVet</span><span class="p">);</span>
 <a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 队列用于实现 BFS</span>
@@ -4044,7 +4048,7 @@
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="k">fn</span> <span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span>: <span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></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>
-<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></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-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></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">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span>::<span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">start_vet</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">// 队列用于实现 BFS</span>
@@ -4148,7 +4152,7 @@
 <a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">()</span>
-<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></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-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</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-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</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">// 队列用于实现 BFS</span>
@@ -4177,7 +4181,7 @@
 <a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><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-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 顶点遍历序列</span>
 <a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></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-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="o">[</span><span class="n">start_vet</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># 队列用于实现 BFS</span>
 <a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">start_vet</span><span class="o">]</span>
@@ -4254,14 +4258,14 @@
 </div>
 <h3 id="2">2. &nbsp; 复杂度分析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
 <p><strong>时间复杂度</strong>：所有顶点都会入队并出队一次，使用 <span class="arithmatex">\(O(|V|)\)</span> 时间；在遍历邻接顶点的过程中，由于是无向图，因此所有边都会被访问 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 时间；总体使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 时间。</p>
-<p><strong>空间复杂度</strong>：列表 <code>res</code> ，哈希表 <code>visited</code> ，队列 <code>que</code> 中的顶点数量最多为 <span class="arithmatex">\(|V|\)</span> ，使用 <span class="arithmatex">\(O(|V|)\)</span> 空间。</p>
+<p><strong>空间复杂度</strong>：列表 <code>res</code> ，哈希集合 <code>visited</code> ，队列 <code>que</code> 中的顶点数量最多为 <span class="arithmatex">\(|V|\)</span> ，使用 <span class="arithmatex">\(O(|V|)\)</span> 空间。</p>
 <h2 id="932">9.3.2 &nbsp; 深度优先遍历<a class="headerlink" href="#932" title="Permanent link">&para;</a></h2>
 <p><strong>深度优先遍历是一种优先走到底、无路可走再回头的遍历方式</strong>。如图 9-11 所示，从左上角顶点出发，访问当前顶点的某个邻接顶点，直到走到尽头时返回，再继续走到尽头并返回，以此类推，直至所有顶点遍历完成。</p>
 <p><a class="glightbox" href="../graph_traversal.assets/graph_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="图的深度优先遍历" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></a></p>
 <p align="center"> 图 9-11 &nbsp; 图的深度优先遍历 </p>

 <h3 id="1_1">1. &nbsp; 算法实现<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>这种“走到尽头再返回”的算法范式通常基于递归来实现。与广度优先遍历类似，在深度优先遍历中，我们也需要借助一个哈希表 <code>visited</code> 来记录已被访问的顶点，以避免重复访问顶点。</p>
+<p>这种“走到尽头再返回”的算法范式通常基于递归来实现。与广度优先遍历类似，在深度优先遍历中，我们也需要借助一个哈希集合 <code>visited</code> 来记录已被访问的顶点，以避免重复访问顶点。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4281,7 +4285,7 @@
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></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-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>    <span class="c1"># 顶点遍历序列</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="c1"># 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="c1"># 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>    <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]()</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">)</span>
 <a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>    <span class="k">return</span> <span class="n">res</span>
@@ -4306,7 +4310,7 @@
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </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="o">&amp;</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="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></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-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">;</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></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-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -4332,7 +4336,7 @@
 <a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></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="nf">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><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></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">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></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-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="n">Set</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;&gt;</span><span class="p">();</span>
 <a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></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-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -4359,7 +4363,7 @@
 <a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></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><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">// 顶点遍历序列</span>
 <a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></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="p">[];</span>
-<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></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-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></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="p">[];</span>
 <a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></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-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -4387,7 +4391,7 @@
 <a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></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-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
 <a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span>
 <a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">    </span><span class="c1">// 返回顶点遍历序列</span>
@@ -4415,7 +4419,7 @@
 <a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="kd">func</span> <span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">startVet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">{</span>
 <a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a>    <span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a>    <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
-<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a>    <span class="c1">// 哈希表，用于记录已被访问过的顶点</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a>    <span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a>    <span class="kd">var</span> <span class="nv">visited</span><span class="p">:</span> <span class="n">Set</span><span class="p">&lt;</span><span class="n">Vertex</span><span class="p">&gt;</span> <span class="p">=</span> <span class="p">[]</span>
 <a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">startVet</span><span class="p">)</span>
 <a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a>    <span class="k">return</span> <span class="n">res</span>
@@ -4443,7 +4447,7 @@
 <a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
-<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></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-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
 <a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
 <a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
@@ -4475,7 +4479,7 @@
 <a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
-<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></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-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o">&lt;</span><span class="nx">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
 <a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
 <a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
@@ -4506,7 +4510,7 @@
 <a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></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><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">  </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></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="p">[];</span>
-<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></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-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">  </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">  </span><span class="n">Set</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="p">{};</span>
 <a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></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-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -4535,7 +4539,7 @@
 <a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="k">fn</span> <span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span>: <span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></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>
-<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></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-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></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">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span>::<span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">);</span>
 <a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a>
@@ -4602,7 +4606,7 @@
 <a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex?)</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">    </span><span class="c1">// 顶点遍历序列</span>
 <a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">()</span>
-<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></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-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">    </span><span class="c1">// 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">()</span>
 <a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></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-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
@@ -4627,7 +4631,7 @@
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">  </span><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-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w">  </span><span class="c1"># 顶点遍历序列</span>
 <a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
-<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></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-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w">  </span><span class="c1"># 哈希集合，用于记录已被访问过的顶点</span>
 <a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w">  </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span>
 <a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></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">start_vet</span><span class="p">)</span>
 <a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w">  </span><span class="n">res</span>
@@ -4699,7 +4703,7 @@
 </div>
 <h3 id="2_1">2. &nbsp; 复杂度分析<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
 <p><strong>时间复杂度</strong>：所有顶点都会被访问 <span class="arithmatex">\(1\)</span> 次，使用 <span class="arithmatex">\(O(|V|)\)</span> 时间；所有边都会被访问 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 时间；总体使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 时间。</p>
-<p><strong>空间复杂度</strong>：列表 <code>res</code> ，哈希表 <code>visited</code> 顶点数量最多为 <span class="arithmatex">\(|V|\)</span> ，递归深度最大为 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空间。</p>
+<p><strong>空间复杂度</strong>：列表 <code>res</code> ，哈希集合 <code>visited</code> 顶点数量最多为 <span class="arithmatex">\(|V|\)</span> ，递归深度最大为 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空间。</p>

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