第六章图完结

图/图的应用/P254.9.cpp

@@ -0,0 +1,131 @@
+#include <iostream>
+#include <stack>
+#include <queue>
+#include <vector>
+#include <algorithm>
+
+using namespace std;
+
+#pragma region 创建邻接表存储的有向图
+
+#define MaxVertexNum 10   //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（v1 -> v2）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;
+    }
+}
+
+#pragma endregion
+
+//P254.9
+//试说明利用DFS如何实现有向无环图拓扑排序
+
+bool visited[MaxVertexNum];
+int topo[MaxVertexNum];
+int j = 0;
+
+void DFS(ALGraph G, int i) {         
+
+    ArcNode* p;
+    visited[i] = true;         		
+    p = G.vertices[i].first;       
+    while (p) {                    
+        if (!visited[p->adjvex])    
+            DFS(G, p->adjvex);
+        p = p->next;
+    }
+    topo[j++] = i;
+}
+
+void DFSTraverse(ALGraph G) {
+
+    memset(visited, false, sizeof(visited));      
+    _for(i, 0, G.vexnum)
+        if (!visited[i])
+            DFS(G, i);	            			
+}
+
+void Print_TopologicalSorting(ALGraph G) {
+    for (int i = G.vexnum - 1; i >= 0; i--) {
+        cout << G.vertices[topo[i]].data << " ";
+    }
+    cout << endl;
+}
+
+
+int main()
+{
+    ALGraph G;
+    CreateALGraph(G);
+    cout << "DFS求拓扑排序:" << endl;
+    DFSTraverse(G);
+    Print_TopologicalSorting(G);
+    return 0;
+}
+
+/*
+input:
+
+6 7
+a b c d e f
+a b
+a d
+c e
+c f
+d b
+e d
+f f
+
+有向图链接：https://s3.ax1x.com/2021/02/23/yLASpT.png
+
+*/