第十一周 【项目4(2) - 利用遍历思想求解图问题】

（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;
}

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73

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;
}

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55

附：测试用图结构