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@ -2992,6 +2992,8 @@
@ -3097,6 +3099,34 @@
<li class="md-nav__item">
<a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
<span class="md-ellipsis">
15.3. &nbsp; 最大容量问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
</ul>
</nav>
@ -3560,7 +3590,44 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">graph_bfs.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="n">class</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.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 广度优先遍历 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></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-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">graphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">t</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-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="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">t</span><span class="o">-&gt;</span><span class="n">size</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="n">memset</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">t</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="c1">// 队列用于实现 BFS</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">*</span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newQueue</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">size</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">// 哈希表，用于记录已被访问过的顶点</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="n">hashTable</span><span class="w"> </span><span class="o">*</span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newHash</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">resIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="n">queuePush</span><span class="p">(</span><span class="n">que</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 将第一个元素入队</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="n">hashMark</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="o">-&gt;</span><span class="n">pos</span><span class="p">);</span><span class="w"> </span><span class="c1">// 标记第一个入队的顶点</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></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-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></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="o">-&gt;</span><span class="n">head</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">que</span><span class="o">-&gt;</span><span class="n">tail</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="c1">// 遍历该顶点的边链表，将所有与该顶点有连接的，并且未被标记的顶点入队</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queueTop</span><span class="p">(</span><span class="n">que</span><span class="p">)</span><span class="o">-&gt;</span><span class="n">linked</span><span class="o">-&gt;</span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="c1">// 查询哈希表，若该索引的顶点已入队，则跳过，否则入队并标记</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashQuery</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="o">-&gt;</span><span class="n">val</span><span class="o">-&gt;</span><span class="n">pos</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></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-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w"> </span><span class="n">queuePush</span><span class="p">(</span><span class="n">que</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="o">-&gt;</span><span class="n">val</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-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w"> </span><span class="n">hashMark</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="o">-&gt;</span><span class="n">val</span><span class="o">-&gt;</span><span class="n">pos</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-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w"> </span><span class="c1">// 队首元素存入数组</span>
<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">resIndex</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queueTop</span><span class="p">(</span><span class="n">que</span><span class="p">);</span><span class="w"> </span><span class="c1">// 队首顶点加入顶点遍历序列</span>
<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w"> </span><span class="n">resIndex</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w"> </span><span class="n">queuePop</span><span class="p">(</span><span class="n">que</span><span class="p">);</span><span class="w"> </span><span class="c1">// 队首元素出队</span>
<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w"> </span><span class="c1">// 释放内存</span>
<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w"> </span><span class="n">freeQueue</span><span class="p">(</span><span class="n">que</span><span class="p">);</span>
<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w"> </span><span class="n">freeHash</span><span class="p">(</span><span class="n">visited</span><span class="p">);</span>
<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w"> </span><span class="n">resIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w"> </span><span class="c1">// 返回顶点遍历序列</span>
<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></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-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3875,9 +3942,40 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">graph_dfs.c</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="n">class</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>
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="n">class</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>
<div class="highlight"><span class="filename">graph_dfs.c</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><span class="kt">int</span><span class="w"> </span><span class="n">resIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="kt">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="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">hashTable</span><span class="w"> </span><span class="o">*</span><span class="n">visited</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">vet</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">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashQuery</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="o">-&gt;</span><span class="n">pos</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="k">return</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-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </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="n">hashMark</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="o">-&gt;</span><span class="n">pos</span><span class="p">);</span><span class="w"> </span><span class="c1">// 标记顶点并将顶点存入数组</span>
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">resIndex</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将顶点存入数组</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="n">resIndex</span><span class="o">++</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="c1">// 遍历该顶点链表</span>
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="o">-&gt;</span><span class="n">linked</span><span class="o">-&gt;</span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="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">n</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">res</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="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="o">-&gt;</span><span class="n">next</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="p">}</span>
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="p">}</span>
<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a>
<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="cm">/* 深度优先遍历 DFS */</span>
<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></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-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">graphAdjList</span><span class="w"> </span><span class="o">*</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-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w"> </span><span class="c1">// 顶点遍历序列</span>
<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w"> </span><span class="n">memset</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</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="c1">// 哈希表，用于记录已被访问过的顶点</span>
<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w"> </span><span class="n">hashTable</span><span class="w"> </span><span class="o">*</span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newHash</span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</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="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">startVet</span><span class="p">,</span><span class="w"> </span><span class="n">res</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="c1">// 释放哈希表内存并将数组索引归零</span>
<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w"> </span><span class="n">freeHash</span><span class="p">(</span><span class="n">visited</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">resIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w"> </span><span class="c1">// 返回遍历数组</span>
<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></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-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="p">}</span>
</code></pre></div>
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