开启图的篇章

2026-06-16 06:57:38 +08:00 · 2021-02-18 21:59:55 +08:00
parent f3da3c3d5c
commit 147e35f4c5
1 changed files with 149 additions and 0 deletions
--- a/图/图的存储及基本操作/P223.4.cpp
+++ b/图/图的存储及基本操作/P223.4.cpp
@@ -0,0 +1,149 @@
+#include <iostream>
+
+using namespace std;
+
+#pragma region 创建邻接表存储的无向图
+
+#define MaxVertexNum 100    //图中顶点数目最大值
+#define VertexType char
+#define _for(i,a,b) for(int i=(a);i<(b);i++)
+
+typedef struct ArcNode {    //边表结点
+    int adjvex;             //该弧所指向的顶点的位置
+    ArcNode* next;          //指向下一条弧的指针
+}ArcNode;
+
+typedef struct VNode {      //顶点表结点
+    VertexType data;        //顶点信息
+    ArcNode* first;         //指向第一条依附该顶点的弧的指针
+}VNode,AdjList[MaxVertexNum];
+
+typedef struct {            
+    AdjList vertices;       //领接表
+    int vexnum, arcnum;     //图的顶点数和弧数
+}ALGraph;                   //ALGraph是以邻接表存储的图类型
+
+
+int LocateVex(ALGraph& G, VertexType x) {
+
+    _for(i, 0, G.vexnum) {
+        if (G.vertices[i].data == x)
+            return i;
+    }
+    return -1;
+}
+
+void CreateALGraph(ALGraph& G) {
+
+    cout << "输入顶点数和边数"<<endl;
+    cin >> G.vexnum >> G.arcnum;
+    _for(i, 0, G.vexnum) {
+        cout << "输入第" << i + 1 << "个顶点的信息" << endl;
+        cin >> G.vertices[i].data;
+        G.vertices[i].first = NULL;
+    }
+    _for(k, 0, G.arcnum) {
+        VertexType e1, e2;
+        cout << "输入第" << k + 1 << "条边的顶点：" << endl;
+        cin >> e1 >> e2;
+        ArcNode* e = new ArcNode;
+        if (!e) {
+            cout << "内存申请失败！" << endl;
+            exit(0);
+        }
+
+        int vi = LocateVex(G, e1);
+        int vj = LocateVex(G, e2);
+
+        e->adjvex = vj;									//这三步，类似于单链表的头插法
+        e->next = G.vertices[vi].first;
+        G.vertices[vi].first = e;
+
+        e = new ArcNode;
+        if (!e) {
+            cout << "内存申请失败！" << endl;
+            exit(0);
+        }
+        e->adjvex = vi;									
+        e->next = G.vertices[vj].first;
+        G.vertices[vj].first = e;
+    }
+}
+
+bool visited[MaxVertexNum];
+
+void DFS(ALGraph G, int i)          //邻接表的深度优先递归
+{
+    ArcNode* p;
+    visited[i] = true;         		//访问过了该顶点，标记为TRUE 
+    cout << G.vertices[i].data << " ";
+    p = G.vertices[i].first;        //让p指向边表第一个结点 
+    while (p) {                     //在边表内遍历 
+        if (!visited[p->adjvex])    //对未访问的邻接顶点递归调用 
+            DFS(G, p->adjvex);
+        p = p->next;
+    }
+}
+
+void DFSTraverse(ALGraph G) {        //邻接表的深度遍历操作
+    _for(i, 0, G.vexnum)
+        visited[i] = false;         //初始设置为未访问 
+    _for(i, 0, G.vexnum)
+        if (!visited[i])
+            DFS(G, i);	            //对未访问的顶点调用DFS，若是连通图只会执行一次 			
+}
+
+#pragma endregion
+
+//P223.4
+//写出从图的邻接表表示转换成邻接矩阵表示的算法。
+
+void Convert(ALGraph& G, int arcs[MaxVertexNum][MaxVertexNum]) {
+    
+    _for(i, 0, G.vexnum) {
+        ArcNode *p = G.vertices[i].first;
+        while (p) {
+            arcs[i][p->adjvex] = 1;
+            p = p->next;
+        }
+    }
+}
+
+int main()
+{
+    int arcs[MaxVertexNum][MaxVertexNum];
+    memset(arcs, 0, sizeof(arcs));
+    ALGraph G;
+    CreateALGraph(G);
+    cout << endl;
+    cout << "DFS:" << endl;
+    DFSTraverse(G);
+    cout << endl;
+    cout << endl;
+    cout <<"转换后的邻接矩阵:"<< endl;
+    Convert(G, arcs);
+    _for(i, 0, G.vexnum) {
+        _for(j, 0, G.vexnum)
+            cout << arcs[i][j] << " ";
+        cout << endl;
+    }
+   
+    return 0;
+}
+
+/*
+input:
+
+5 7
+a b c d e
+a b
+a e
+b c
+b d
+b e
+c d
+d e
+
+
+生成图的链接：https://s3.ax1x.com/2021/02/18/yW59vF.png
+*/