第十一周 【项目4(2)

（程序中graph.h是图存储结构的“算法库”中的头文件，详情请单击链接…）

1、最短路径 
问题：求不带权连通图G中从顶点u到顶点v的一条最短路径。

#include <stdio.h>#include <malloc.h>#include "graph.h"typedef struct{    int data;                   //顶点编号    int parent;                 //前一个顶点的位置} QUERE;                        //非环形队列类型void ShortPath(ALGraph *G,int u,int v){    //输出从顶点u到顶点v的最短逆路径    ArcNode *p;    int w,i;    QUERE qu[MAXV];             //非环形队列    int front=-1,rear=-1;       //队列的头、尾指针    int visited[MAXV];    for (i=0; i<G->n; i++)      //访问标记置初值0        visited[i]=0;    rear++;                     //顶点u进队    qu[rear].data=u;    qu[rear].parent=-1;    visited[u]=1;    while (front!=rear)         //队不空循环    {        front++;                //出队顶点w        w=qu[front].data;        if (w==v)               //找到v时输出路径之逆并退出        {            i=front;            //通过队列输出逆路径            while (qu[i].parent!=-1)            {                printf("%2d ",qu[i].data);                i=qu[i].parent;            }            printf("%2d\n",qu[i].data);            break;        }        p=G->adjlist[w].firstarc;   //找w的第一个邻接点        while (p!=NULL)        {            if (visited[p->adjvex]==0)            {                visited[p->adjvex]=1;                rear++;             //将w的未访问过的邻接点进队                qu[rear].data=p->adjvex;                qu[rear].parent=front;            }            p=p->nextarc;           //找w的下一个邻接点        }    }}int main(){    ALGraph *G;    int A[9][9]=    {        {0,1,1,0,0,0,0,0,0},        {0,0,0,1,1,0,0,0,0},        {0,0,0,0,1,1,0,0,0},        {0,0,0,0,0,0,1,0,0},        {0,0,0,0,0,1,1,0,0},        {0,0,0,0,0,0,0,1,0},        {0,0,0,0,0,0,0,1,1},        {0,0,0,0,0,0,0,0,1},        {0,0,0,0,0,0,0,0,0}    };  //请画出对应的有向图    ArrayToList(A[0], 9, G);    ShortPath(G,0,7);    return 0;}
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附：测试用图结构 

2、最远顶点 
问题：求不带权连通图G中，距离顶点v最远的顶点k

#include <stdio.h>#include <malloc.h>#include "graph.h"int Maxdist(ALGraph *G,int v){    ArcNode *p;    int i,j,k;    int Qu[MAXV];               //环形队列    int visited[MAXV];              //访问标记数组    int front=0,rear=0;             //队列的头、尾指针    for (i=0; i<G->n; i++)          //初始化访问标志数组        visited[i]=0;    rear++;    Qu[rear]=v;                 //顶点v进队    visited[v]=1;               //标记v已访问    while (rear!=front)    {        front=(front+1)%MAXV;        k=Qu[front];                //顶点k出队        p=G->adjlist[k].firstarc;       //找第一个邻接点        while (p!=NULL)             //所有未访问过的相邻点进队        {            j=p->adjvex;            //邻接点为顶点j            if (visited[j]==0)          //若j未访问过            {                visited[j]=1;                rear=(rear+1)%MAXV;                Qu[rear]=j; //进队            }            p=p->nextarc;           //找下一个邻接点        }    }    return k;}int main(){    ALGraph *G;    int A[9][9]=    {        {0,1,1,0,0,0,0,0,0},        {0,0,0,1,1,0,0,0,0},        {0,0,0,0,1,1,0,0,0},        {0,0,0,0,0,0,1,0,0},        {0,0,0,0,0,1,1,0,0},        {0,0,0,0,0,0,0,1,0},        {0,0,0,0,0,0,0,1,1},        {0,0,0,0,0,0,0,0,1},        {0,0,0,0,0,0,0,0,0}    };  //请画出对应的有向图    ArrayToList(A[0], 9, G);    printf("离顶点0最远的顶点:%d",Maxdist(G,0));    return 0;}
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附：测试用图结构