图的拓扑排序，广度和深度优先搜索

图：邻接表表示方法 如下为无圈图

1.图的拓扑排序，用来判断图中是否有圈，例如学生的选课系统，当你选择一门课程时需要一系列的基础课程，而这些课程都是有序安排的，但是如果在这些课程当中有圈存在的话，会存在学生不断循环去选择这些课程，多次选择相同课程。所以而这种情况是不被允许的。

2.图的深度优先搜索，一般用于找无向图的割点(删除某点后，图将不再连通)。图的广度优先搜索类似与树的层序遍历(level-order),它则用于无权图的最短路径求法。

//函数接口

#ifndef _TOPSORT_H#define _TOPSORT_H#define MAX 20typedef struct EdgeNode{int vex;struct EdgeNode *next;}ENode;typedef struct VexNode{char data;ENode *first;}VNode;typedef struct graph{int vexnum;int edgenum;VNode vexs[MAX];}Graph;void CreateGraph(Graph *g);int TopSort(Graph G);void Destroy(Graph *g);void DFSTraverse(Graph G);void BFSTraverse(Graph G);#endif

//接口函数定义

#include <stdio.h>#include <string.h>#include "topsort.h"#include <stdlib.h>#define MAX 20int visited[MAX];static void DFS(Graph G,int edge);int TopSort(Graph G){int i,j;int index=0; //统计拓扑排序过的总点数 最后判断有无圈int head=0;  //队列头尾初始化int rear=0;int *queue;int *indegree;char *tops;int num=G.vexnum;ENode *node;indegree=(int *)malloc(num*sizeof(int));tops=(char *)malloc(num*sizeof(char));queue=(int *)malloc(num*sizeof(int)); //用数组来建立队列memset(indegree,0,num*sizeof(int));  //memset来初始化动态数组memset(tops,0,num*sizeof(char));memset(queue,0,num*sizeof(int));for(i=0;i<num;i++){node=G.vexs[i].first;while(node!=NULL){indegree[node->vex]++; //统计入度node=node->next;}}for(i=0;i<num;i++){if(indegree[i]==0)queue[rear++]=i; //i入队}while(head<rear){j=queue[head++];  //j出队tops[index++]=G.vexs[j].data;node=G.vexs[j].first;while(node!=NULL){indegree[node->vex]--; //入度减1if(indegree[node->vex]==0)queue[rear++]=node->vex; //邻接点入队node=node->next; //与node邻接的下个节点}}if(index!=G.vexnum){printf("Graph has a cycle!!");free(indegree);    free(tops);    free(queue);return 1;}else{printf("TopSort:\n");for(i=0;i<num;i++)printf("%2c",tops[i]);printf("\n");    free(indegree);    free(tops);    free(queue);return 0;}}void CreateGraph(Graph *g){char ver;int i=0;int e=-1;ENode *edge;printf("Enter vexnum and edgenum:\n");scanf("%d %d",&g->vexnum,&g->edgenum);getchar();printf("Enter the data of vertex:\n");while('\n'!=(ver=getchar()))g->vexs[i++].data=ver;for(i=0;i<g->vexnum;i++)  //Graph初始化g->vexs[i].first=NULL;printf("Enter the edge table:\n");for(i=0;i<g->vexnum;i++){printf("%c:",g->vexs[i].data);while(1){scanf("%d",&e);if(e!=-1){edge=(ENode *)malloc(sizeof(ENode));    edge->vex=e;    edge->next=g->vexs[i].first;    g->vexs[i].first=edge;}else  //用-1来退出循环break;}printf("\n");}}static void DFS(Graph G,int edge){ENode *e;visited[edge]=1; //将访问过的节点置为1printf("%2c",G.vexs[edge].data);e=G.vexs[edge].first;while(e){if(!visited[e->vex])DFS(G,e->vex);e=e->next;}}void DFSTraverse(Graph G)  //深度优先搜索 递归实现{int i;for(i=0;i<G.vexnum;i++)visited[i]=0; //标记数组初始化for(i=0;i<G.vexnum;i++){if(!visited[i])DFS(G,i);}}void BFSTraverse(Graph G) //广度优先搜索{int i,tmp;ENode *e;int queue[MAX];int rear,front;rear=front=0;for(i=0;i<=G.vexnum;i++)visited[i]=0; //标记数组初始化for(i=0;i<G.vexnum;i++){if(!visited[i]){visited[i]=1;printf("%2c",G.vexs[i].data);queue[rear++]=i; //入队while(front<rear){tmp=queue[front++];//出队e=G.vexs[tmp].first;while(e){if(!visited[e->vex]){visited[e->vex]=1;printf("%2c",G.vexs[e->vex].data);queue[rear++]=e->vex;}e=e->next;}}}}}void Destroy(Graph *g){int i;ENode *e,*tmp;for(i=0;i<g->vexnum;i++){e=g->vexs[i].first;while(e!=NULL){tmp=e;e=e->next;free(tmp);}}}

//main函数入口

#include <stdio.h>#include "topsort.h"int main(int argc, char **argv){Graph G;CreateGraph(&G);TopSort(G);printf("\nDFSTraverse\n");DFSTraverse(G);printf("\nBFSTraverse\n");BFSTraverse(G);Destroy(&G);return 0;}

测试结果：