图的最短路径-优快云博客

本文介绍了图的基本存储结构及深度优先搜索与广度优先搜索的实现方法，并演示了最短路径算法的具体步骤。通过定义不同的图类型，如有向图、无向图等，展示了如何创建图并进行节点定位，最后给出了最短路径算法的实现。

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#include <stdio.h>
#include <string.h>
#define INFINITY 1000
#define MAX_VERTEX_NUM 20
typedef enum{DG,DN,UDG,UDN} Graphkind;
typedef struct ArcCell{
int adj;
char *info;
}ArcCell,AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
typedef struct{
char vexs[MAX_VERTEX_NUM][4];
AdjMatrix arcs;
int vexnum,arcnum;
Graphkind kind;
}MGraph;
int visited[MAX_VERTEX_NUM];
void CreateGraph(MGraph *G);
void CreateDG(MGraph *G);
void CreateDN(MGraph *G);
void CreateUDG(MGraph *G);
void CreateUDN(MGraph *G);
int LocateVex(MGraph *G,char v[4]);
void Girst_next_adj(MGraph *G,int i);
void dfs1(MGraph *G,int i);
void bfs1(MGraph *G,int i);
void shortesPath_DIJ(MGraph *G,int v0,int p[][MAX_VERTEX_NUM],int d[MAX_VERTEX_NUM]);
#define QUEUE_INIT_SIZE 100
#define QUEUEINCREMENT 10
typedef int QElemType;
typedef struct{
QElemType *elem;
int front;
int rear;
int queuesize;
int incrementsize;
}SqQueue;
void InitQueue_sq(SqQueue *Q,int n);
int QueueLength_Sq(SqQueue Q);
int DeQueue_Sq(SqQueue *Q,QElemType *e);
void incrementQueuesize(SqQueue *Q);
void EnQueue_Sq(SqQueue *Q,QElemType e);
int GetQueue_Sq(SqQueue Q,QElemType *e);
int QueueEmpty(SqQueue Q);
main(){
MGraph G;
int i,j;
char v[4];
int p[MAX_VERTEX_NUM][MAX_VERTEX_NUM],d[MAX_VERTEX_NUM];
       CreateGraph(&G);
for(i=0;i<G.vexnum;++i)
{
    for(j=0;j<G.vexnum;++j)
     printf("%8d",G.arcs[i][j].adj);
    putchar('\n');
}
printf("输入深度优先搜索初始顶点Vi: ");
getchar();
scanf("%s",v);
i=LocateVex(&G,v);
dfs1(&G,i);
printf("\n输入出发广度优先搜索初始顶点: ");
getchar();
scanf("%s",v);
       i=LocateVex(&G,v);
bfs1(&G,v);
bfs1(&G,i);
if(G->kind==DN||G->kind=UDN)
{
    printf("\n输入查找第一邻接点的顶点： ");
    getchar();
    scanf("%s",v);
    i=LocateVex(&G,v);
    shortesPath_DIJ(&G,0,p,d);
}
}
int visited[MAX_VERTEX_NUM];
void dfs1(MGraph *G,int i)
{
int j;
printf("%5s",G->vexs[i]);
visited[i]=1;
for(j=0;j<G->vexnum;j++)
    if(i!=j&&G->arcs[i][j].adj!=INFINITY&&!visited[j])
     dfs1(G,j);
}
void bfs1(MGraph *G,int i)
{
int k,j;
SqQueue Q;
for(j=0;j<G->vexnum;j++)
    visited[j]=0;
InitQueue_Sq(&Q,G->vexnum);
printf("\n%5s",G->vexs[i]);
visited[i]=1;
EnQueue_Sq(&Q,i);
while(!QueueEmpty(Q))
{
    DeQueue_Sq(&Q,&k);
    for(j=0;j<G->vexnum;j++)
    {
     if(k!j&&G->arcs[k][j].adj!=INFINITY&&!visited[j])
     {
      printf("%5s",G->vexs[j]);
      visited[j]=1;
      EnQueue_Sq(&Q,j);
     }
    }
}
}
int LocateVex(MGraph *G,char v[4])
{
int i=0;
while(i<G->vexnum)
{
    if(strcmp(G->vexs[i],v)==0) return i;
            i++;
}
printf("\n输入的顶点不存在！");
return 0;
}
void CreateDG(MGraph *G)
{}
void CreateDN(MGraph *G)
{
int i,j,k,w;
char v1[4],v2[4];
printf("输入DN--vexnum,arcnum:");
scanf("%d%d",&G-<vexnum,&G->arcnum);
printf("输入vexs[i]:\n");
getchar();
for(i=0;i<G->vexnum;++i)
    gets(G->vexs[i]);
for(i=0;i<G->vexnum;++i)
        switch(k)
{
    case 0:G->kind=DG; break;
    case 1:G->kind=DN; break;
    case 2:G->kind=UDG; break;
    case 3:G->kind=UDN; break;
}
switch(G->kind)
{
case DG:CreateDG(G); break;
case DN:CreateDN(G); break;
case UDG:CreateUDG(G); break;
case UDN:CreateUDN(G); break;
}
printf("ok!\n");
}
void First_next_adj(MGraph *G,int i)
{
int j;
for(j=0;j<G->arcs[i][j].adj!=INFINITY)
    if(G->arcs[i][j].adj!=INFINITY)
       printf("%s\n",G->vexs[j]);
}

void shortesPath_DIJ(MGraph *G,int v0,intp[][MAX_VERTEX_NUM],int d[MAX_VERTEX_NUM]){
 int i,j,v,min,w,final[MAX_VERTEX_NUM],v1,w1;
 for(v=0;v<g->vexnum;++v){
    final[v]=0;
    d[v]=G->arcs[v0][v].adj;
    for(w=0;w<G->vexnum;++w)
     p[v][w]=0;
    if(d[v]<INFINITY){
     p[v][v0]=1;p[v][v]=1;
    }
 }
 printf("\nfinal[]:");
 for(v1=0;v1<G->vexnum;++v1)
    printf("%6d",final[v1]);
 printf("\n\n      d[]:     ");
 for(v1=0;v1<G->vexnum;++v1)
    printf("%6d",d[v1]);
 printf("\n\np[][]:\n");
 for(v1=0;v1<G->vexnum;++v1){
    for(w1=0;w1<G->vexnum;++w1)
     printf("%6d",p[v1][w1]);
    putchar('\n');
 }
 d[v0]=0;final[v0]=1;
 for(i=1;i<G->vexnum;++i){
    min=INFINITY;
    for(w=0;w<G->vexnum;++w)
     if(!final[w])
      if(d[w]<min){
       v=w;
       min=d[w];
      }
      final[v]=1;
      for(w=0;w<G->vexnum;++w)
       if(!final[w]&&(min+G->arcs[v][w].adj<d[w])){
        d[w]=min+G->arcs[v][w].adj;
        for(j=0;j<G->vexnum;++j)
         p[w][j]=p[v][j];
        q[w][w]=1;
       }
       printf("\nfinal[]:");
       for(v1=0;v1<G->vexnum;++v1)
        printf("%6d",final[v1];
       printf("\n\n      d[]:      ");
           for(v1=0;v1<G->vexnum;++v1)
        printf("%6d",d[v1]);
       printf("\n\np[][]:\n");
       for(v1=0;v1<G->vexnum;++v1){
        for(w1=0;w1<G->vexnum;++w1)
         printf"%6d",p[v1][w1]);
        putchar('\n');
       }
 }
}