data_structure/17_Graph_Storage.html at main · sunluyong/data_structure · GitHub

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<!DOCTYPE html>
<html lang="zh-CN">
  <head>
    <meta charset="UTF-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <title>17 图的存储：邻接矩阵与邻接表</title>
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  <body>
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    <div id="app" class="slide-container">
      <div class="bg-decoration"></div>
      <div class="grid-overlay"></div>

      <!-- P01: 封面 -->
      <section class="slide active justify-center items-center text-center" data-title="封面">
        <div class="flex flex-col items-center z-10 relative -mt-32">
          <!-- 图标放在最上面 -->
          <div class="mb-12 flex gap-8">
            <div class="flex flex-col items-center">
                <div class="w-24 h-24 border-2 border-accent grid grid-cols-3 gap-1 p-1 rounded-lg bg-accent/10">
                    <div class="bg-accent/50"></div><div class="bg-accent/20"></div><div class="bg-accent/50"></div>
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                    <div class="bg-accent/50"></div><div class="bg-accent/20"></div><div class="bg-accent/50"></div>
                </div>
                <span class="mt-4 text-slate-300 text-xl font-mono">Matrix</span>
            </div>
            <div class="flex flex-col items-center">
                <div class="w-24 h-24 border-2 border-secondary flex flex-col justify-around p-2 rounded-lg bg-secondary/10">
                    <div class="h-4 w-full bg-secondary/50 rounded flex"><div class="w-4 h-4 bg-white rounded-full ml-auto"></div></div>
                    <div class="h-4 w-3/4 bg-secondary/50 rounded flex"><div class="w-4 h-4 bg-white rounded-full ml-auto"></div></div>
                    <div class="h-4 w-1/2 bg-secondary/50 rounded flex"><div class="w-4 h-4 bg-white rounded-full ml-auto"></div></div>
                </div>
                <span class="mt-4 text-slate-300 text-xl font-mono">List</span>
            </div>
          </div>

          <div class="bg-purple-500/10 px-6 py-2 rounded-full border border-purple-500/30 mb-6">
            <span class="text-purple-400 text-2xl font-mono tracking-widest">GRAPH STORAGE</span>
          </div>
          <h1>数据结构与算法</h1>
          <p class="text-[56px] text-secondary">图的存储：邻接矩阵 & 邻接表</p>
        </div>
      </section>

      <!-- P02: 存储的核心问题 -->
      <section class="slide" data-title="核心问题">
        <h2>为什么要讨论存储？</h2>
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                <div class="card border-l-8 border-warn p-8">
                    <h3 class="text-warn text-[40px] mb-4">核心挑战</h3>
                    <p class="text-[32px] text-white leading-relaxed">
                        图的结构比线性表和树更复杂：<br/>
                        <span class="text-slate-300">任意两个顶点都可能相关联。</span>
                    </p>
                </div>
                <div class="card bg-slate-800/30 p-8">
                    <h3 class="text-slate-200 text-[32px] mb-6">我们需要权衡：</h3>
                    <ul class="space-y-6">
                        <li class="flex items-center text-[28px]">
                            <i class="fas fa-hdd w-12 text-center text-accent"></i>
                            <span class="text-slate-200">空间复杂度：存下所有边需要多少内存？</span>
                        </li>
                        <li class="flex items-center text-[28px]">
                            <i class="fas fa-bolt w-12 text-center text-secondary"></i>
                            <span class="text-slate-200">时间复杂度：判断两点是否相连有多快？</span>
                        </li>
                        <li class="flex items-center text-[28px]">
                            <i class="fas fa-list-ol w-12 text-center text-tertiary"></i>
                            <span class="text-slate-200">遍历效率：找到某个点的所有邻居有多快？</span>
                        </li>
                    </ul>
                </div>
            </div>
            <div class="flex flex-col justify-center items-center relative">
                <!-- Visual Metaphor -->
                <div class="relative w-[500px] h-[500px]">
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                        <div class="text-center">
                            <div class="text-[60px] font-bold text-white mb-2">Trade-off</div>
                            <div class="text-[30px] text-slate-300">时间 vs 空间</div>
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                    <div class="absolute top-0 left-1/2 -translate-x-1/2 -translate-y-1/2 bg-bg-dark px-4 text-accent text-2xl font-mono">Dense Graph</div>
                    <div class="absolute bottom-0 left-1/2 -translate-x-1/2 translate-y-1/2 bg-bg-dark px-4 text-secondary text-2xl font-mono">Sparse Graph</div>
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        </div>
      </section>

      <!-- P03: 邻接矩阵 - 概念 -->
      <section class="slide" data-title="邻接矩阵：概念">
        <h2>邻接矩阵：有向图 (Directed)</h2>
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                    <h3 class="text-accent text-[36px] mb-4">定义</h3>
                    <p class="text-[28px] text-slate-200 leading-relaxed">
                        使用一个 <strong class="text-white">二维数组</strong> <span class="font-mono text-accent">G[N][N]</span> 来表示顶点之间的连接关系。
                    </p>
                    <ul class="mt-6 space-y-4 text-[26px] text-slate-300">
                        <li>• 若顶点 <span class="font-mono text-accent">i</span> 和 <span class="font-mono text-accent">j</span> 之间有边，则 <span class="font-mono text-accent">G[i][j] = 1</span> (或权重)。</li>
                        <li>• 若无边，则 <span class="font-mono text-accent">G[i][j] = 0</span> (或 ∞)。</li>
                    </ul>
                </div>

                <div class="mt-6 card p-6 border-slate-700 bg-slate-800/30">
                    <h3 class="text-white text-[30px] mb-4">特点</h3>
                    <ul class="space-y-3 text-[26px] text-slate-300">
                        <li><i class="fas fa-check text-green-500 mr-2"></i> <strong class="text-white">查边快</strong>：O(1) 判断两点是否相连。</li>
                        <li><i class="fas fa-check text-green-500 mr-2"></i> <strong class="text-white">算度快</strong>：行和=出度，列和=入度。</li>
                        <li><i class="fas fa-exclamation-triangle text-warn mr-2"></i> <strong class="text-white">耗空间</strong>：固定 O(V²)，适合稠密图。</li>
                    </ul>
                </div>
            </div>

            <div class="flex flex-col items-center justify-center bg-slate-900/50 rounded-3xl border border-slate-700 p-8">
                <div class="flex gap-12 items-center">
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                    <!-- Arrow -->
                    <div class="text-4xl text-slate-400"><i class="fas fa-arrow-right"></i></div>

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                        <!-- Controls -->
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                            <button onclick="prevMatrixStep()" class="btn-secondary text-xs py-1 px-3">Prev</button>
                            <button onclick="resetMatrixStep()" class="btn-secondary text-xs py-1 px-3">Reset</button>
                            <button onclick="nextMatrixStep()" class="btn-primary text-xs py-1 px-3">Next</button>
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            </div>
        </div>
      </section>

      <!-- P03b: 邻接矩阵 - 无向图 -->
      <section class="slide" data-title="邻接矩阵：无向图">
        <h2>邻接矩阵：无向图 (Undirected)</h2>
        <div class="grid grid-cols-2 gap-12 flex-1 min-h-0">
            <div class="flex flex-col justify-center">
                <div class="card p-8 border-slate-700 bg-slate-800/30">
                    <h3 class="text-white text-[36px] mb-6">对称性 (Symmetry)</h3>
                    <p class="text-[28px] text-slate-200 leading-relaxed">
                        无向图的边没有方向，<span class="font-mono text-accent">(i, j)</span> 等同于 <span class="font-mono text-accent">(j, i)</span>。
                    </p>
                    <ul class="mt-8 space-y-6 text-[26px] text-slate-300">
                        <li><i class="fas fa-check text-green-500 mr-4"></i> 矩阵关于<strong class="text-white">主对角线</strong>对称。</li>
                        <li><i class="fas fa-check text-green-500 mr-4"></i> <span class="font-mono text-accent">G[i][j] == G[j][i]</span></li>
                        <li><i class="fas fa-info-circle text-blue-400 mr-4"></i> 存储时可以只存上三角或下三角以节省空间。</li>
                    </ul>
                </div>
            </div>

            <div class="flex flex-col items-center justify-center bg-slate-900/50 rounded-3xl border border-slate-700 p-8">
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                        <!-- Controls -->
                        <div class="flex gap-4 mt-6">
                            <button onclick="prevUndirectedStep()" class="btn-secondary text-xs py-1 px-3">Prev</button>
                            <button onclick="resetUndirectedStep()" class="btn-secondary text-xs py-1 px-3"> Reset</button>
                            <button onclick="nextUndirectedStep()" class="btn-primary text-xs py-1 px-3">Next</button>
                        </div>
                    </div>
                </div>
                <p class="mt-8 text-slate-300 text-center text-[24px]">同时也更新对称位置，保持矩阵对称。</p>
            </div>
        </div>
      </section>

      <!-- P04: 邻接矩阵 - 代码 -->
      <section class="slide" data-title="邻接矩阵：代码">
        <h2>邻接矩阵：代码实现</h2>
        <div class="grid grid-cols-2 gap-8 flex-1 min-h-0">
            <div class="flex flex-col h-full min-h-0">
                <div class="code-block h-full custom-scrollbar text-[20px]"><span class="code-kw">#define</span> MAX_V 100
<span class="code-kw">#define</span> INF 65535  <span class="code-cm">// 表示无穷大（无边）</span>

<span class="code-kw">typedef struct</span> {
    <span class="code-type">char</span> V[MAX_V];           <span class="code-cm">// 顶点表</span>
    <span class="code-type">int</span> Edge[MAX_V][MAX_V];  <span class="code-cm">// 邻接矩阵 (边表)</span>
    <span class="code-type">int</span> numV, numE;          <span class="code-cm">// 当前顶点数和边数</span>
} <span class="code-type">MGraph</span>;

<span class="code-type">void</span> <span class="code-kw">CreateMGraph</span>(<span class="code-type">MGraph</span> *G) {
    <span class="code-type">int</span> i, j, k, w;

    <span class="code-cm">// 1. 输入顶点数和边数</span>
    <span class="code-kw">printf</span>(<span class="code-str">"输入顶点数和边数: "</span>);
    <span class="code-kw">scanf</span>(<span class="code-str">"%d,%d"</span>, &G->numV, &G->numE);

    <span class="code-cm">// 2. 初始化邻接矩阵</span>
    <span class="code-kw">for</span>(i = 0; i < G->numV; i++) {
        <span class="code-kw">for</span>(j = 0; j < G->numV; j++) {
            <span class="code-kw">if</span> (i == j) G->Edge[i][j] = 0;
            <span class="code-kw">else</span> G->Edge[i][j] = INF;
        }
    }

    <span class="code-cm">// 3. 建立边 (读入边的数据)</span>
    <span class="code-kw">for</span>(k = 0; k < G->numE; k++) {
        <span class="code-kw">printf</span>(<span class="code-str">"输入边(vi,vj)的下标i,j和权重w: "</span>);
        <span class="code-kw">scanf</span>(<span class="code-str">"%d,%d,%d"</span>, &i, &j, &w);

        G->Edge[i][j] = w;
        G->Edge[j][i] = w; <span class="code-cm">// 无向图需对称赋值</span>
    }
} </div>
            </div>
            <div class="flex flex-col justify-center gap-8">
                <div class="card bg-slate-800/30 p-8 border-l-8 border-accent">
                    <h3 class="text-white text-[32px] mb-4">关键点解析</h3>
                    <ul class="space-y-6 text-[28px] text-slate-200">
                        <li><strong class="text-accent">初始化</strong>：所有边初始化为 <span class="font-mono text-warn">INF</span> (或0)，对角线为0。</li>
                        <li><strong class="text-accent">对称性</strong>：无向图 <span class="font-mono">G->Edge[i][j] = G->Edge[j][i]</span>。</li>
                        <li><strong class="text-accent">下标映射</strong>：实际应用中通常需要一个 Map 将顶点名映射为数组下标 0, 1, 2...</li>
                    </ul>
                </div>
                <div class="card bg-slate-800/30 p-8 border-l-8 border-warn">
                    <h3 class="text-white text-[32px] mb-4">适用场景</h3>
                    <p class="text-[28px] text-slate-200">
                        适用于 <strong class="text-white">稠密图 (Dense Graph)</strong>，即边数接近顶点数的平方 (<span class="font-mono">E ≈ V²</span>)。
                    </p>
                </div>
            </div>
        </div>
      </section>

      <!-- P05: 邻接表 - 概念 -->
      <section class="slide" data-title="邻接表：概念">
        <h2>2. 邻接表 (Adjacency List)</h2>
        <div class="grid grid-cols-2 gap-12 flex-1 min-h-0">
            <div class="flex flex-col">
                <div class="card p-8 border-slate-700 bg-slate-800/30">
                    <h3 class="text-secondary text-[36px] mb-4">定义</h3>
                    <p class="text-[28px] text-slate-200 leading-relaxed">
                        数组与链表的结合。每个顶点建立一个<strong class="text-white">单链表</strong>，链表中存储该顶点的所有邻居。
                    </p>
                    <ul class="mt-6 space-y-4 text-[26px] text-slate-300">
                        <li>• 顶点数组 <span class="font-mono text-secondary">AdjList[N]</span> 存储表头。</li>
                        <li>• 链表节点存储邻接点下标 <span class="font-mono text-secondary">adjvex</span> 和权重 <span class="font-mono text-secondary">weight</span>。</li>
                    </ul>
                </div>

                <div class="mt-6 card p-6 border-slate-700 bg-slate-800/30">
                    <h3 class="text-white text-[30px] mb-4">特点</h3>
                    <ul class="space-y-3 text-[26px] text-slate-300">
                        <li><i class="fas fa-check text-green-500 mr-2"></i> 节省空间，只存实际存在的边。</li>
                        <li><i class="fas fa-check text-green-500 mr-2"></i> 空间复杂度 <strong class="text-secondary">O(V + E)</strong>。</li>
                        <li><i class="fas fa-exclamation-triangle text-warn mr-2"></i> 无向图中每条边存储两次 (A->B, B->A)。</li>
                    </ul>
                </div>
            </div>

            <div class="flex flex-col items-center justify-center bg-slate-900/50 rounded-3xl border border-slate-700 p-8 w-full">
                <div class="flex gap-8 items-start w-full justify-center">
                    <!-- Graph Visualization -->
                    <svg width="280" height="280" viewBox="0 0 300 300" class="overflow-visible flex-shrink-0" id="list-graph">
                        <g id="list-edges"></g>
                        <g id="list-nodes"></g>
                    </svg>

                    <!-- Arrow -->
                    <div class="text-4xl text-slate-400 self-center"><i class="fas fa-arrow-right"></i></div>

                    <!-- List Visualization -->
                    <div class="flex flex-col items-start flex-grow min-w-0">
                        <div class="flex flex-col gap-3 w-full" id="list-container">
                            <!-- Lists will be injected here -->
                        </div>
                        <!-- Controls -->
                        <div class="flex gap-4 mt-6 self-center">
                            <button onclick="prevListStep()" class="btn-secondary text-xs py-1 px-3">Prev</button>
                            <button onclick="resetListStep()" class="btn-secondary text-xs py-1 px-3">Reset</button>
                            <button onclick="nextListStep()" class="btn-primary text-xs py-1 px-3">Next</button>
                        </div>
                    </div>
                </div>
            </div>
        </div>
      </section>

      <!-- P05b: 邻接表 - 无向图 -->
      <section class="slide" data-title="邻接表：无向图">
        <h2>邻接表：无向图 (Undirected)</h2>
        <div class="grid grid-cols-2 gap-12 flex-1 min-h-0">
            <div class="flex flex-col">
                <div class="card p-8 border-slate-700 bg-slate-800/30">
                    <h3 class="text-secondary text-[36px] mb-4">冗余存储</h3>
                    <p class="text-[28px] text-slate-200 leading-relaxed">
                        无向图的边 <span class="font-mono text-white">(i, j)</span> 没有方向，需要在两个顶点的链表中分别存储。
                    </p>
                    <ul class="mt-6 space-y-4 text-[26px] text-slate-300">
                        <li>• 在 <span class="font-mono text-secondary">AdjList[i]</span> 中插入节点 <span class="font-mono text-white">j</span>。</li>
                        <li>• 在 <span class="font-mono text-secondary">AdjList[j]</span> 中插入节点 <span class="font-mono text-white">i</span>。</li>
                    </ul>
                </div>

                <div class="mt-6 card p-6 border-slate-700 bg-slate-800/30">
                    <h3 class="text-white text-[30px] mb-4">影响</h3>
                    <ul class="space-y-3 text-[26px] text-slate-300">
                        <li><i class="fas fa-info-circle text-blue-400 mr-2"></i> 边表节点总数是边数的 <strong class="text-white">2倍</strong> (2E)。</li>
                        <li><i class="fas fa-check text-green-500 mr-2"></i> 容易求顶点的度（链表长度即为度）。</li>
                    </ul>
                </div>
            </div>

            <div class="flex flex-col items-center justify-center bg-slate-900/50 rounded-3xl border border-slate-700 p-8 w-full">
                <div class="flex gap-8 items-start w-full justify-center">
                    <!-- Graph Visualization -->
                    <svg width="280" height="280" viewBox="0 0 300 300" class="overflow-visible flex-shrink-0" id="ulist-graph">
                        <g id="ulist-edges"></g>
                        <g id="ulist-nodes"></g>
                    </svg>

                    <!-- Arrow -->
                    <div class="text-4xl text-slate-400 self-center"><i class="fas fa-arrow-right"></i></div>

                    <!-- List Visualization -->
                    <div class="flex flex-col items-start flex-grow min-w-0">
                        <div class="flex flex-col gap-3 w-full" id="ulist-container">
                            <!-- Lists will be injected here -->
                        </div>
                        <!-- Controls -->
                        <div class="flex gap-4 mt-6 self-center">
                            <button onclick="prevUListStep()" class="btn-secondary text-xs py-1 px-3">Prev</button>
                            <button onclick="resetUListStep()" class="btn-secondary text-xs py-1 px-3">Reset</button>
                            <button onclick="nextUListStep()" class="btn-primary text-xs py-1 px-3">Next</button>
                        </div>
                    </div>
                </div>
            </div>
        </div>
      </section>

      <!-- P06: 邻接表 - 代码 -->
      <section class="slide" data-title="邻接表：代码">
        <h2>邻接表：代码实现</h2>
        <div class="grid grid-cols-2 gap-8 flex-1 min-h-0">
            <div class="flex flex-col h-full min-h-0">
                <div class="code-block h-full custom-scrollbar text-[18px]"><span class="code-kw">typedef struct</span> EdgeNode {
    <span class="code-type">int</span> adjvex;              <span class="code-cm">// 邻接点下标</span>
    <span class="code-type">int</span> weight;              <span class="code-cm">// 权重</span>
    <span class="code-kw">struct</span> EdgeNode *next;   <span class="code-cm">// 指向下一个邻接点</span>
} <span class="code-type">EdgeNode</span>;

<span class="code-kw">typedef struct</span> VertexNode {
    <span class="code-type">char</span> data;               <span class="code-cm">// 顶点信息</span>
    <span class="code-type">EdgeNode</span> *firstedge;     <span class="code-cm">// 边表头指针</span>
} <span class="code-type">VertexNode</span>, <span class="code-type">AdjList</span>[MAX_V];

<span class="code-kw">typedef struct</span> {
    <span class="code-type">AdjList</span> adjList;
    <span class="code-type">int</span> numV, numE;
} <span class="code-type">GraphAdjList</span>;

<span class="code-type">void</span> <span class="code-kw">CreateALGraph</span>(<span class="code-type">GraphAdjList</span> *G) {
    <span class="code-type">int</span> i, j, k;
    <span class="code-type">EdgeNode</span> *e;
    <span class="code-kw">scanf</span>(<span class="code-str">"%d,%d"</span>, &G->numV, &G->numE);

    <span class="code-cm">// 初始化顶点表</span>
    <span class="code-kw">for</span>(i = 0; i < G->numV; i++) {
        <span class="code-kw">scanf</span>(<span class="code-str">"%c"</span>, &G->adjList[i].data);
        G->adjList[i].firstedge = <span class="code-kw">NULL</span>;
    }

    <span class="code-cm">// 头插法建立边表</span>
    <span class="code-kw">for</span>(k = 0; k < G->numE; k++) {
        <span class="code-kw">scanf</span>(<span class="code-str">"%d,%d"</span>, &i, &j);

        e = (<span class="code-type">EdgeNode</span> *)<span class="code-kw">malloc</span>(<span class="code-kw">sizeof</span>(<span class="code-type">EdgeNode</span>));
        e->adjvex = j;
        e->next = G->adjList[i].firstedge;
        G->adjList[i].firstedge = e;

        <span class="code-cm">// 无向图需重复一次 (j -> i)</span>
        e = (<span class="code-type">EdgeNode</span> *)<span class="code-kw">malloc</span>(<span class="code-kw">sizeof</span>(<span class="code-type">EdgeNode</span>));
        e->adjvex = i;
        e->next = G->adjList[j].firstedge;
        G->adjList[j].firstedge = e;
    }
}</div>
            </div>
            <div class="flex flex-col justify-center gap-8">
                <div class="card bg-slate-800/30 p-8 border-l-8 border-secondary">
                    <h3 class="text-white text-[32px] mb-4">关键点解析</h3>
                    <ul class="space-y-6 text-[28px] text-slate-200">
                        <li><strong class="text-secondary">结构体嵌套</strong>：EdgeNode (边) 挂在 VertexNode (点) 下。</li>
                        <li><strong class="text-secondary">头插法</strong>：新边插入链表头部，O(1) 速度，但导致邻居顺序与输入相反。</li>
                        <li><strong class="text-secondary">出度容易，入度难</strong>：求入度需要遍历整个图（或者使用逆邻接表）。</li>
                    </ul>
                </div>
                <div class="card bg-slate-800/30 p-8 border-l-8 border-warn">
                    <h3 class="text-white text-[32px] mb-4">适用场景</h3>
                    <p class="text-[28px] text-slate-200">
                        适用于 <strong class="text-white">稀疏图 (Sparse Graph)</strong>，即边数远小于顶点数的平方。
                    </p>
                </div>
            </div>
        </div>
      </section>

      <!-- P07: 对比总结 -->
      <section class="slide" data-title="对比总结">
        <h2>哪种存储更好？</h2>
        <div class="flex flex-col items-center justify-center flex-1 min-h-0 w-full">
            <div class="w-full max-w-[1600px] overflow-hidden rounded-3xl border border-slate-700 shadow-2xl">
                <table class="w-full text-left border-collapse">
                    <thead>
                        <tr class="bg-slate-800 text-white text-[32px]">
                            <th class="p-6 border-b border-slate-600">特性</th>
                            <th class="p-6 border-b border-slate-600 text-accent">邻接矩阵 (Matrix)</th>
                            <th class="p-6 border-b border-slate-600 text-secondary">邻接表 (List)</th>
                        </tr>
                    </thead>
                    <tbody class="text-[28px] text-slate-200 bg-slate-900/50">
                        <tr class="hover:bg-slate-800/50 transition-colors">
                            <td class="p-6 border-b border-slate-700 font-bold text-white">空间复杂度</td>
                            <td class="p-6 border-b border-slate-700 font-mono text-warn">O(V²)</td>
                            <td class="p-6 border-b border-slate-700 font-mono text-green-400">O(V + E)</td>
                        </tr>
                        <tr class="hover:bg-slate-800/50 transition-colors">
                            <td class="p-6 border-b border-slate-700 font-bold text-white">判断两点连接</td>
                            <td class="p-6 border-b border-slate-700 font-mono text-green-400">O(1)</td>
                            <td class="p-6 border-b border-slate-700 font-mono text-warn">O(Degree)</td>
                        </tr>
                        <tr class="hover:bg-slate-800/50 transition-colors">
                            <td class="p-6 border-b border-slate-700 font-bold text-white">找所有邻居</td>
                            <td class="p-6 border-b border-slate-700 font-mono text-warn">O(V)</td>
                            <td class="p-6 border-b border-slate-700 font-mono text-green-400">O(Degree)</td>
                        </tr>
                        <tr class="hover:bg-slate-800/50 transition-colors">
                            <td class="p-6 border-b border-slate-700 font-bold text-white">适用场景</td>
                            <td class="p-6 border-b border-slate-700">稠密图，需要快速判断边的存在</td>
                            <td class="p-6 border-b border-slate-700">稀疏图，频繁增删节点</td>
                        </tr>
                        <tr class="hover:bg-slate-800/50 transition-colors">
                            <td class="p-6 font-bold text-white">实现难度</td>
                            <td class="p-6 text-green-400">简单 (数组)</td>
                            <td class="p-6 text-warn">中等 (指针操作)</td>
                        </tr>
                    </tbody>
                </table>
            </div>

            <div class="mt-12 flex gap-8">
                <div class="bg-blue-900/20 border border-blue-500/30 px-8 py-4 rounded-xl">
                    <p class="text-[28px] text-blue-300"><i class="fas fa-lightbulb mr-3"></i> <strong>十字链表</strong>：解决有向图求入度难的问题。</p>
                </div>
                <div class="bg-blue-900/20 border border-blue-500/30 px-8 py-4 rounded-xl">
                    <p class="text-[28px] text-blue-300"><i class="fas fa-lightbulb mr-3"></i> <strong>邻接多重表</strong>：优化无向图边的操作。</p>
                </div>
            </div>
        </div>
      </section>

      <!-- P08: 小结 -->
      <section class="slide" data-title="小结">
        <h2>本节小结</h2>
        <div class="flex items-center justify-center flex-1 min-h-0">
            <div class="card p-10 border-slate-700 bg-slate-800/30 w-2/3">
                <ul class="space-y-8 text-[36px]">
                    <li class="flex items-start">
                        <span class="w-12 h-12 rounded-full bg-accent flex items-center justify-center text-white text-xl font-bold mr-6 mt-1">1</span>
                        <span><strong class="text-white">邻接矩阵</strong>用二维数组，适合稠密图，查边快 <span class="font-mono text-accent">O(1)</span>，但费空间。</span>
                    </li>
                    <li class="flex items-start">
                        <span class="w-12 h-12 rounded-full bg-secondary flex items-center justify-center text-white text-xl font-bold mr-6 mt-1">2</span>
                        <span><strong class="text-white">邻接表</strong>用链表数组，适合稀疏图，省空间 <span class="font-mono text-secondary">O(V+E)</span>，但查边慢。</span>
                    </li>
                    <li class="flex items-start">
                        <span class="w-12 h-12 rounded-full bg-tertiary flex items-center justify-center text-white text-xl font-bold mr-6 mt-1">3</span>
                        <span>算法选择存储结构时，要根据<strong class="text-white">图的规模</strong>和<strong class="text-white">操作类型</strong>来决定。</span>
                    </li>
                </ul>
                <div class="mt-16 text-center">
                    <p class="text-[32px] text-slate-400">Next : 图的遍历 (BFS & DFS)</p>
                </div>
            </div>
        </div>
      </section>

      <!-- Page Number -->
      <div id="page-number" class="absolute bottom-6 right-8 text-slate-400 text-[24px] font-mono z-50"></div>
    </div>

    <script>
      let currentSlide = 0;
      const pageNumberEl = document.getElementById('page-number');

      const urlParams = new URLSearchParams(window.location.search);
      if (urlParams.has('page')) {
        const page = parseInt(urlParams.get('page'));
        if (!isNaN(page) && page > 0) currentSlide = page - 1;
      }

      function updateSlide() {
        const slides = document.querySelectorAll('.slide');
        if (currentSlide >= slides.length) currentSlide = slides.length - 1;
        if (currentSlide < 0) currentSlide = 0;

        slides.forEach((slide, index) => {
          slide.classList.remove('active');
          if (index === currentSlide) {
            slide.classList.add('active');
            // Init demos if needed
            const title = slide.getAttribute('data-title');
            if (title === '邻接矩阵：概念') {
                if(document.getElementById('matrix-grid').children.length === 0) {
                    initDirectedDemo();
                }
            } else if (title === '邻接矩阵：无向图') {
                if(document.getElementById('undirected-grid').children.length === 0) {
                    initUndirectedDemo();
                }
            } else if (title === '邻接表：概念') {
                if(document.getElementById('list-container').children.length === 0) {
                    initListDemo();
                }
            } else if (title === '邻接表：无向图') {
                if(document.getElementById('ulist-container').children.length === 0) {
                    initUListDemo();
                }
            }
          }
        });

        if(pageNumberEl) pageNumberEl.textContent = `${currentSlide + 1} / ${slides.length}`;

        try {
          const url = new URL(window.location.href);
          url.searchParams.set('page', currentSlide + 1);
          window.history.replaceState(null, '', url.href);
        } catch (e) {}
      }

      function nextSlide() {
        if (currentSlide < document.querySelectorAll('.slide').length - 1) {
            currentSlide++;
            updateSlide();
        }
      }

      function prevSlide() {
        if (currentSlide > 0) {
            currentSlide--;
            updateSlide();
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      }

      function resizeApp() {
        const app = document.getElementById('app');
        const scale = Math.min(window.innerWidth / 1920, window.innerHeight / 1080);
        app.style.transform = `scale(${scale})`;
      }

      window.addEventListener('resize', resizeApp);
      window.addEventListener('load', () => {
        resizeApp();
        updateSlide();
      });
      document.addEventListener('keydown', (e) => {
        if (['ArrowRight', ' ', 'Enter'].includes(e.key)) nextSlide();
        else if (e.key === 'ArrowLeft') prevSlide();
      });

      // --- Matrix Animation Logic (Directed & Undirected) ---

      // --- Directed Graph Data ---
      const directedData = {
          nodes: [
              { id: 0, x: 150, y: 40 },
              { id: 1, x: 260, y: 120 },
              { id: 2, x: 220, y: 250 },
              { id: 3, x: 80, y: 250 },
              { id: 4, x: 40, y: 120 }
          ],
          edges: [
              [0, 1], [1, 2], [2, 3], [3, 4], [4, 0], // Cycle
              [0, 2], [1, 4] // Cross edges
          ]
      };

      // --- Undirected Graph Data ---
      const undirectedData = {
          nodes: [
              { id: 0, x: 150, y: 40 },
              { id: 1, x: 260, y: 120 },
              { id: 2, x: 220, y: 250 },
              { id: 3, x: 80, y: 250 },
              { id: 4, x: 40, y: 120 }
          ],
          edges: [
              [0, 1], [1, 2], [2, 3], [3, 4], [4, 0],
              [0, 2], [1, 4]
          ]
      };

      let directedStep = 0;
      let undirectedStep = 0;

      // --- Directed Functions ---
      function initDirectedDemo() {
          const svgEdges = document.getElementById('matrix-edges');
          const svgNodes = document.getElementById('matrix-nodes');
          const grid = document.getElementById('matrix-grid');

          if(!svgEdges || !svgNodes || !grid) return;

          svgEdges.innerHTML = '';
          svgNodes.innerHTML = '';
          grid.innerHTML = '';

          // Draw Edges
          directedData.edges.forEach((edge, index) => {
              const [u, v] = edge;
              const uNode = directedData.nodes[u];
              const vNode = directedData.nodes[v];

              const dx = vNode.x - uNode.x;
              const dy = vNode.y - uNode.y;
              const length = Math.sqrt(dx*dx + dy*dy);
              const padding = 25;

              const x2 = vNode.x - (dx / length) * padding;
              const y2 = vNode.y - (dy / length) * padding;

              const line = document.createElementNS("http://www.w3.org/2000/svg", "line");
              line.id = `directed-edge-${index}`;
              line.setAttribute('x1', uNode.x);
              line.setAttribute('y1', uNode.y);
              line.setAttribute('x2', x2);
              line.setAttribute('y2', y2);
              line.setAttribute('stroke', '#334155');
              line.setAttribute('stroke-width', '2');
              line.setAttribute('marker-end', 'url(#arrow-matrix)');
              line.style.transition = 'stroke 0.3s';
              svgEdges.appendChild(line);
          });

          // Draw Nodes
          directedData.nodes.forEach(node => {
              const g = document.createElementNS("http://www.w3.org/2000/svg", "g");
              g.innerHTML = `
                  <circle cx="${node.x}" cy="${node.y}" r="20" fill="#4c1d95" stroke="#8b5cf6" stroke-width="2"/>
                  <text x="${node.x}" y="${node.y + 6}" text-anchor="middle" fill="#fff" font-size="16" font-weight="bold">${node.id}</text>
              `;
              svgNodes.appendChild(g);
          });

          // Draw Matrix
          const corner = document.createElement('div');
          grid.appendChild(corner);
          for(let i=0; i<5; i++) {
              const h = document.createElement('div');
              h.className = 'text-accent font-bold w-12 h-12 flex items-center justify-center';
              h.textContent = i;
              grid.appendChild(h);
          }
          for(let i=0; i<5; i++) {
              const h = document.createElement('div');
              h.className = 'text-accent font-bold w-12 h-12 flex items-center justify-center';
              h.textContent = i;
              grid.appendChild(h);
              for(let j=0; j<5; j++) {
                  const cell = document.createElement('div');
                  cell.id = `directed-cell-${i}-${j}`;
                  cell.className = 'bg-slate-800 w-12 h-12 flex items-center justify-center rounded text-slate-500 border-2 border-transparent transition-all duration-300';
                  cell.textContent = (i === j) ? '0' : '∞';
                  grid.appendChild(cell);
              }
          }
          updateDirectedVisuals();
      }

      function updateDirectedVisuals() {
          for(let i=0; i<directedData.edges.length; i++) {
              const line = document.getElementById(`directed-edge-${i}`);
              if(line) {
                  line.setAttribute('stroke', i < directedStep ? '#8b5cf6' : '#334155');
              }
          }
          for(let i=0; i<5; i++) {
              for(let j=0; j<5; j++) {
                  const cell = document.getElementById(`directed-cell-${i}-${j}`);
                  if(cell) {
                      let isActive = false;
                      for(let k=0; k<directedStep; k++) {
                          const [u, v] = directedData.edges[k];
                          if(u === i && v === j) isActive = true;
                      }
                      if(isActive) {
                          cell.textContent = '1';
                          cell.className = 'bg-purple-900/80 text-white w-12 h-12 flex items-center justify-center rounded border-2 border-purple-500 transition-all duration-300';
                      } else {
                          cell.textContent = (i === j) ? '0' : '∞';
                          cell.className = 'bg-slate-800 text-slate-500 w-12 h-12 flex items-center justify-center rounded border-2 border-transparent transition-all duration-300';
                      }
                  }
              }
          }
      }

      function nextMatrixStep() {
          if(directedStep < directedData.edges.length) {
              directedStep++;
              updateDirectedVisuals();
          }
      }
      function prevMatrixStep() {
          if(directedStep > 0) {
              directedStep--;
              updateDirectedVisuals();
          }
      }
      function resetMatrixStep() {
          directedStep = 0;
          updateDirectedVisuals();
      }

      // --- Undirected Functions ---
      function initUndirectedDemo() {
          const svgEdges = document.getElementById('undirected-edges');
          const svgNodes = document.getElementById('undirected-nodes');
          const grid = document.getElementById('undirected-grid');

          if(!svgEdges || !svgNodes || !grid) return;

          svgEdges.innerHTML = '';
          svgNodes.innerHTML = '';
          grid.innerHTML = '';

          // Draw Edges
          undirectedData.edges.forEach((edge, index) => {
              const [u, v] = edge;
              const uNode = undirectedData.nodes[u];
              const vNode = undirectedData.nodes[v];

              const line = document.createElementNS("http://www.w3.org/2000/svg", "line");
              line.id = `undirected-edge-${index}`;
              line.setAttribute('x1', uNode.x);
              line.setAttribute('y1', uNode.y);
              line.setAttribute('x2', vNode.x);
              line.setAttribute('y2', vNode.y);
              line.setAttribute('stroke', '#334155');
              line.setAttribute('stroke-width', '2');
              line.style.transition = 'stroke 0.3s';
              svgEdges.appendChild(line);
          });

          // Draw Nodes
          undirectedData.nodes.forEach(node => {
              const g = document.createElementNS("http://www.w3.org/2000/svg", "g");
              g.innerHTML = `
                  <circle cx="${node.x}" cy="${node.y}" r="20" fill="#4c1d95" stroke="#8b5cf6" stroke-width="2"/>
                  <text x="${node.x}" y="${node.y + 6}" text-anchor="middle" fill="#fff" font-size="16" font-weight="bold">${node.id}</text>
              `;
              svgNodes.appendChild(g);
          });

          // Draw Matrix
          const corner = document.createElement('div');
          grid.appendChild(corner);
          grid.classList.add('relative');
          for(let i=0; i<5; i++) {
              const h = document.createElement('div');
              h.className = 'text-accent font-bold w-12 h-12 flex items-center justify-center';
              h.textContent = i;
              grid.appendChild(h);
          }
          for(let i=0; i<5; i++) {
              const h = document.createElement('div');
              h.className = 'text-accent font-bold w-12 h-12 flex items-center justify-center';
              h.textContent = i;
              grid.appendChild(h);
              for(let j=0; j<5; j++) {
                  const cell = document.createElement('div');
                  cell.id = `undirected-cell-${i}-${j}`;
                  cell.className = 'bg-slate-800 w-12 h-12 flex items-center justify-center rounded text-slate-500 border-2 border-transparent transition-all duration-300';
                  cell.textContent = (i === j) ? '0' : '∞';
                  grid.appendChild(cell);
              }
          }

          // Add Overlay for Lower Triangle Shadow & Diagonal Line
          const overlay = document.createElement('div');
          overlay.className = 'absolute pointer-events-none z-10';
          overlay.style.top = '52px';
          overlay.style.left = '52px';
          overlay.style.width = '256px';
          overlay.style.height = '256px';
          // Gradient: Bottom-Left (Dark) -> Top-Right (Transparent)
          overlay.style.background = 'linear-gradient(45deg, rgba(3,7,18,0.5) 50%, transparent 0%)';
          grid.appendChild(overlay);

          updateUndirectedVisuals();
      }

      function updateUndirectedVisuals() {
          for(let i=0; i<undirectedData.edges.length; i++) {
              const line = document.getElementById(`undirected-edge-${i}`);
              if(line) {
                  line.setAttribute('stroke', i < undirectedStep ? '#8b5cf6' : '#334155');
              }
          }
          for(let i=0; i<5; i++) {
              for(let j=0; j<5; j++) {
                  const cell = document.getElementById(`undirected-cell-${i}-${j}`);
                  if(cell) {
                      let isActive = false;
                      for(let k=0; k<undirectedStep; k++) {
                          const [u, v] = undirectedData.edges[k];
                          // Check both directions
                          if((u === i && v === j) || (u === j && v === i)) isActive = true;
                      }
                      if(isActive) {
                          cell.textContent = '1';
                          cell.className = 'bg-purple-900/80 text-white w-12 h-12 flex items-center justify-center rounded border-2 border-purple-500 transition-all duration-300';
                      } else {
                          cell.textContent = (i === j) ? '0' : '∞';
                          cell.className = 'bg-slate-800 text-slate-500 w-12 h-12 flex items-center justify-center rounded border-2 border-transparent transition-all duration-300';
                      }
                  }
              }
          }
      }

      function nextUndirectedStep() {
          if(undirectedStep < undirectedData.edges.length) {
              undirectedStep++;
              updateUndirectedVisuals();
          }
      }
      function prevUndirectedStep() {
          if(undirectedStep > 0) {
              undirectedStep--;
              updateUndirectedVisuals();
          }
      }
      function resetUndirectedStep() {
          undirectedStep = 0;
          updateUndirectedVisuals();
      }

      // Initialize on load
      window.addEventListener('load', () => {
         setTimeout(() => {
             // 强制触发一次 updateSlide 以确保当前页面的图被初始化
             updateSlide();
         }, 100);
      });

      // --- List Animation Logic ---
      let listStep = 0;

      // Re-ordered edges for "Node-by-Node" processing (Head Insertion)
      const listDemoEdges = [
          [0, 1], [0, 2], // Node 0's edges
          [1, 2], [1, 4], // Node 1's edges
          [2, 3],         // Node 2's edges
          [3, 4],         // Node 3's edges
          [4, 0]          // Node 4's edges
      ];

      function initListDemo() {
          const svgEdges = document.getElementById('list-edges');
          const svgNodes = document.getElementById('list-nodes');
          const listContainer = document.getElementById('list-container');

          if(!svgEdges || !svgNodes || !listContainer) return;

          svgEdges.innerHTML = '';
          svgNodes.innerHTML = '';
          listContainer.innerHTML = '';

          // Draw Edges (Graph) - Draw ALL edges initially
          directedData.edges.forEach((edge) => {
              const [u, v] = edge;
              const uNode = directedData.nodes[u];
              const vNode = directedData.nodes[v];

              const dx = vNode.x - uNode.x;
              const dy = vNode.y - uNode.y;
              const length = Math.sqrt(dx*dx + dy*dy);
              const padding = 25;

              const x2 = vNode.x - (dx / length) * padding;
              const y2 = vNode.y - (dy / length) * padding;

              const line = document.createElementNS("http://www.w3.org/2000/svg", "line");
              // Use u-v based ID for easier lookup
              line.id = `list-edge-${u}-${v}`;
              line.setAttribute('x1', uNode.x);
              line.setAttribute('y1', uNode.y);
              line.setAttribute('x2', x2);
              line.setAttribute('y2', y2);
              line.setAttribute('stroke', '#334155');
              line.setAttribute('stroke-width', '2');
              line.setAttribute('marker-end', 'url(#arrow-matrix)');
              line.style.transition = 'stroke 0.3s';
              svgEdges.appendChild(line);
          });

          // Draw Nodes (Graph)
          directedData.nodes.forEach(node => {
              const g = document.createElementNS("http://www.w3.org/2000/svg", "g");
              g.innerHTML = `
                  <circle cx="${node.x}" cy="${node.y}" r="20" fill="#4c1d95" stroke="#8b5cf6" stroke-width="2"/>
                  <text x="${node.x}" y="${node.y + 6}" text-anchor="middle" fill="#fff" font-size="16" font-weight="bold">${node.id}</text>
              `;
              svgNodes.appendChild(g);
          });

          // Initialize List Structure (Heads)
          for(let i=0; i<5; i++) {
              const row = document.createElement('div');
              row.className = 'flex items-center h-14';
              row.id = `list-row-${i}`;