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124 lines
2.9 KiB
124 lines
2.9 KiB
///////////////////////////////////////
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/// file: algraph.h
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/// 邻接表与图的遍历
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///////////////////////////////////////
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#pragma once
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#include <stdexcept>
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using std::length_error;
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using std::invalid_argument;
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///////////////////////////////////////
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/// 存储结构
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///
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/// 图的邻接表(Adjacency-List)存储结构
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///
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template <typename V, typename E, int M = 20>
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struct ALGraph
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{
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// 弧结点结构
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struct ArcNode
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{
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E weight; // 弧上的权值
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int adjvex; // 邻接点（弧头）
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ArcNode *nextarc; // 指向下一个弧结点（同弧尾的）
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};
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// 顶点结点结构
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struct VexNode
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{
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V data; // 顶点数据
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ArcNode *firstarc; // 指向第一个弧结点（以该顶点为弧尾的）
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};
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VexNode vexs[M]; // 图中的顶点
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int vexnum, arcnum; // 顶点和弧的数量
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bool visited[M]; // 顶点访问标志
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};
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///////////////////////////////////////
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/// 基本操作
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///
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/// 初始化图
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///
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template <typename V, typename E, int M>
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void InitGraph(ALGraph<V, E, M> &G)
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{
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G.vexnum = 0;
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G.arcnum = 0;
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}
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///
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/// 添加顶点
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///
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template <typename V, typename E, int M>
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int AddVertex(ALGraph<V, E, M> &G, V v)
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{
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if (G.vexnum == M)
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throw std::length_error("Too many vertex");
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int i = G.vexnum;
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G.vexs[i].data = v;
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G.vexs[i].firstarc = nullptr;
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G.vexnum++;
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return i;
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}
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///
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/// 添加边
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///
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template <typename V, typename E, int M>
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void AddEdge(ALGraph<V, E, M> &G, int s, int t, E e = 1)
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{
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if (s < 0 || s >= G.vexnum)
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throw std::invalid_argument("Invalid source vertex");
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if (t < 0 || t >= G.vexnum)
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throw std::invalid_argument("Invalid target vertex");
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using ArcNode = typename ALGraph<V, E, M>::ArcNode;
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auto p = new ArcNode;
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p->weight = e;
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p->adjvex = t;
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p->nextarc = G.vexs[s].firstarc;
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G.vexs[s].firstarc = p;
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G.arcnum++;
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}
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///
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/// 从顶点 v 出发深度优先遍历图 G
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///
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template <typename V, typename E, int M, typename F>
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void DFS(ALGraph<V, E, M> &G, int v, F visit)
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{
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// 访问顶点 v
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visit(G.vexs[v].data);
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G.visited[v] = true;
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// 从顶点 v 的未被访问的邻接点 w 开始继续深度优先搜索
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for (auto p = G.vexs[v].firstarc; p; p = p->nextarc)
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{
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auto w = p->adjvex;
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if (!G.visited[w])
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DFS(G, w, visit);
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}
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}
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///
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/// 深度优先搜索遍历图 G
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///
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template <typename V, typename E, int M, typename F>
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void DFSTraverse(ALGraph<V, E, M> &G, F visit)
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{
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// 初始化顶点访问标志 visited
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for (int v = 0; v < G.vexnum; ++v)
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G.visited[v] = false;
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// 从一个未访问的顶点 v 出发深度优先遍历图 G
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for (int v = 0; v < G.vexnum; ++v)
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if (!G.visited[v])
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DFS(G, v, visit);
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}
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