拓扑排序

拓扑排序是针对有向无环图。
拓扑排序算法主要是循环执行以下两步，直到不存在入度为0的顶点为止。

(1) 选择一个入度为0的顶点并输出之；

(2) 从网中删除此顶点及所有出边。

循环结束后，若输出的顶点数小于网中的顶点数，则输出“有回路”信息，否则输出的顶点序列就是一种拓扑序列。

简单实现：

#include<iostream>#define MVNum 100//表示最大顶点数using namespace std;typedef struct ArcNode//边结点{int adjvex;//该边所指向顶点的位置 下标struct ArcNode *nextarc;//指向下一条边的指针}ArcNode;typedef struct VNode//顶点信息{int data;ArcNode *firstarc;//指向第一条依附于该顶点的边的指针}VNode, AdjList[MVNum];typedef struct//邻接表{AdjList vertices;int vexnum, arcnum;//图的当前顶点数和边数}DAGraph;typedef struct StackNode{int data;struct StackNode *next;}StackNode,*LinkStack;void InitStack(LinkStack &S){S = NULL;}int Pop(LinkStack &S,int &e){StackNode *p;e = S->data;p = S;S = S->next;delete p;return e;}void Push(LinkStack &S, int e){//cout << "b" << endl;StackNode *p;p = new StackNode;p->data = e;p->next = S;S = p;}int StackEmpty(LinkStack S){if (S == NULL)return 1;elsereturn 0;}int Get_Position(DAGraph G, int ch){int i;for (i = 0; i<G.vexnum; i++)if (G.vertices[i].data == ch)return i;return -1;}DAGraph *Create_Graph(){DAGraph *G1;int i, s, d, a, b;ArcNode *p1;G1 = new DAGraph;cout << "请输入总顶点数：" << endl;cin >> G1->vexnum;cout << "请输入总边数：" << endl;cin >> G1->arcnum;cout << "输入顶点：" << endl;for (i = 0; i < G1->vexnum; ++i){cin >> G1->vertices[i].data;G1->vertices[i].firstarc = NULL;}//   for (i = 0; i < G1->vexnum; ++i)//{//cout << G1->vertices[i].data << " ";//G1->vertices[i].firstarc = NULL;//}//cout<<endl;for (i = 0; i < G1->arcnum; ++i){cout << "输入一条边的起点和终点：" << endl;cin >> s >> d;a = Get_Position(*G1, s);b = Get_Position(*G1, d);p1 = new ArcNode;p1->adjvex = b;p1->nextarc = G1->vertices[a].firstarc;G1->vertices[a].firstarc = p1;cout << "e" << endl;//tiaoshi}//   for (int i = 0; i < G1->arcnum; ++i){//       cout << "Node:" <<i<<"->";//       ArcNode *p1 = G1->vertices[i].firstarc;//       while(p1){//         cout << p1->adjvex <<" ";//         p1 = p1->nextarc;//       }//       cout<<endl;//   }return G1;}void TopologicalSort(DAGraph G){int i, m, k;int topo[100] = {0};int indegree[100] = {0};ArcNode *p,*q;LinkStack S;InitStack(S);for (i = 0; i < G.vexnum; i++)//统计每一个结点的入度{q = G.vertices[i].firstarc;while (q != NULL){         int index = q->adjvex;indegree[index]++;q = q->nextarc;}}for (i = 0; i < G.vexnum; ++i)if (!indegree[i])Push(S, i);m = 0;//cout << "a" << endl;//tioaoshiwhile (StackEmpty(S) == 0){Pop(S, i);topo[m] = i;//cout << "i" << i << endl;//tiaoshi++m;//cout << "a" << endl;//tioaoship = G.vertices[i].firstarc;//cout << "d" << endl;//tiaoshiwhile (p != NULL){//cout << "c" << endl;k = p->adjvex;--indegree[k];if (indegree[k] == 0)Push(S, k);p = p->nextarc;}}if (m < G.vexnum)cout << "该有向图有回路" << endl;else{cout << "拓扑排序为：" << endl;for (i = 0; i < m; i++){cout << topo[i]+1 << " ";}}}int main(){DAGraph *G;G=Create_Graph();TopologicalSort(*G);return 0;}