图的遍历。

数据结构。

上机实验：图的深度优先搜索遍历和广度优先搜索遍历。拓扑排序。

测试数据：

6 8
A B C D E F
A B
A C
A D
C E
C B
C E
D E
F D
F E

测试结果：

请输入图的顶点数，边数：6 8
请输入6个顶点的值：
A B C D E F
请输入8条弧的弧尾 弧头：
A B
A C
A D
C E
C B
C E
D E
F D
深度优先搜索遍历的结果为：
A D E C B F


广度优先搜索遍历的结果为：
A D C B E F


F A C B D E 为一个拓扑序列。

#include <stdio.h>#include <stdlib.h>#define MAX_VERTEX_NUM 20//最大顶点数#define stackinitsize 100#define stackincrement 10#define ok 1#define error 0#define overflow -1typedef char VertexType;//顶点类型typedef int status;typedef int SElemType;  //定义栈元素为整型typedef int QElemType;//定义队列元素为整型 struct ElemType{int adjvex;//该弧所指向的顶点的位置,无其他弧信息 };typedef struct ArcNode//表结点，存弧的信息 {ElemType data;//除指针以外的部分都属于ElemType ArcNode *nextarc;//指向下一条弧的指针 }ArcNode,*parcnode;typedef struct//头结点，存顶点的信息 {VertexType data;//顶点信息 ArcNode *firstarc;//第1个表结点的地址，指向第1条依附该顶点的弧的指针 }VNode,AdjList[MAX_VERTEX_NUM];struct ALGraph//邻接表结构{AdjList vertices;//头结点（顶点）数组 int vexnum,arcnum;//图的当前顶点数和弧数 };//栈的操作typedef struct SqStack{SElemType *base;SElemType *top;int stacksize;}SqStack;status InitStack(SqStack &S){S.base = (SElemType *)(malloc)(stackinitsize * sizeof(SElemType));if(!S.base) exit(overflow);S.top=S.base;S.stacksize=stackinitsize;return ok;}status Push(SqStack &S,SElemType e){if(S.top - S.base >= S.stacksize){S.base = (SElemType *)realloc(S.base,(S.stacksize + stackincrement)*sizeof(SElemType));if(!S.base) exit(overflow);S.top=S.base + S.stacksize;S.stacksize += stackincrement;}*S.top++ =e;return ok;}status Pop(SqStack &S,SElemType &e){if(S.top==S.base) return error;e =*--S.top;return ok;}status StackEmpty(SqStack S){if(S.top==S.base) return 1;else return 0;}//链队列的操作typedef struct QNode{QElemType data;QNode *next;}*QueuePtr;struct LinkQueue{QueuePtr front,rear;};void InitQueue(LinkQueue &Q){Q.front=Q.rear=(QueuePtr)malloc(sizeof(QNode));if(!Q.front)exit(overflow);Q.front->next=NULL;}status QueueEmpty(LinkQueue &Q){if(Q.front->next==NULL)return 1;elsereturn 0;}void EnQueue(LinkQueue &Q,QElemType e){QueuePtr p;p=(QueuePtr)malloc(sizeof(QNode));if(!p) exit(overflow);p->data=e;p->next=NULL;Q.rear->next=p;Q.rear=p;}status DeQueue(LinkQueue &Q,QElemType &e){QueuePtr p;if(Q.front==Q.rear) return error;p=Q.front->next;e=p->data;Q.front->next=p->next;if(Q.rear==p)Q.rear=Q.front;free(p);return ok;}//图的操作bool visited[MAX_VERTEX_NUM]; //访问标记数组 void ListInsert(parcnode &L,int i,ElemType e)//插入函数 {parcnode s;s=(ArcNode *)malloc(sizeof(ArcNode));s->data=e;s->nextarc=L;L=s;}int LocateVex(ALGraph G,VertexType u){int i;for(i=0;i<G.vexnum;++i){if(G.vertices[i].data==u) return i;}return -1;}void CreateGraph(ALGraph &G)//采用邻接表存储结构，构造有向图 {int i,j,k;ElemType e;VertexType v1,v2;printf("请输入图的顶点数，边数：");scanf("%d%d",&G.vexnum,&G.arcnum);getchar();printf("请输入%d个顶点的值：\n",G.vexnum);for(i=0;i<G.vexnum;++i){scanf("%c",&G.vertices[i].data);getchar();G.vertices[i].firstarc=NULL;}printf("请输入%d条弧的弧尾 弧头：\n",G.arcnum);for(k=0;k<G.arcnum;++k){scanf("%c %c",&v1,&v2);getchar();i=LocateVex(G,v1);//弧头 j=LocateVex(G,v2);//弧尾e.adjvex=j;ListInsert(G.vertices[i].firstarc,1,e);}}void Visit(VertexType e){printf("%c ",e);}void DFS(ALGraph G,int v,void(*Visit)(VertexType))//深度优先搜索遍历{ArcNode *p;visited[v]=true;Visit(G.vertices[v].data);for(p=G.vertices[v].firstarc;p;p=p->nextarc)if(!visited[p->data.adjvex])DFS(G,p->data.adjvex,Visit);}void DFSTraverse(ALGraph G,void(*Visit)(VertexType)){int v;for(v=0;v<G.vexnum;++v)visited[v]=false;for(v=0;v<G.vexnum;++v){if(!visited[v])DFS(G,v,Visit);}printf("\n\n");}void BFSTraverse(ALGraph G,void(*Visit)(VertexType))//广度优先搜索遍历{ArcNode *p;LinkQueue Q;int v,u;for(v=0;v<G.vexnum;++v)visited[v]=false;InitQueue(Q);for(v=0;v<G.vexnum;++v){if(!visited[v]){ visited[v]=true;Visit(G.vertices[v].data);EnQueue(Q,v);while(!QueueEmpty(Q)){DeQueue(Q,u);for(p=G.vertices[u].firstarc;p;p=p->nextarc)if(!visited[p->data.adjvex]){visited[p->data.adjvex]=true;Visit(G.vertices[p->data.adjvex].data);EnQueue(Q,p->data.adjvex);}}} }printf("\n\n");}//拓扑排序 int indegree[MAX_VERTEX_NUM];void FindInDegree(ALGraph G){int i;ArcNode *p;for(i=0;i<G.vexnum;++i)indegree[i]=0;for(i=0;i<G.vexnum;++i){p=G.vertices[i].firstarc;while(p){indegree[p->data.adjvex]++;p=p->nextarc;}}}status TopologicalSort(ALGraph G){int i,k,count=0;SqStack S;ArcNode *p;FindInDegree(G);InitStack(S);for(i=0;i<G.vexnum;++i)if(!indegree[i])Push(S,i);while(!StackEmpty(S)){Pop(S,i);Visit(G.vertices[i].data);++count;for(p=G.vertices[i].firstarc;p;p=p->nextarc){k=p->data.adjvex;if(!(--indegree[k]))Push(S,k);}}if(count<G.vexnum){printf("此图存在回路\n");return error;}else{printf("为一个拓扑序列。\n");return ok;}}int main(){ALGraph g;CreateGraph(g);printf("深度优先搜索遍历的结果为：\n");DFSTraverse(g,Visit);printf("广度优先搜索遍历的结果为：\n");BFSTraverse(g,Visit);TopologicalSort(g);return 0;}