最小生成树poj2421 Constructing Roads

http://poj.org/problem?id=2421

Description

There are N villages, which are numbered from 1 to N, and you should build some roads such that every two villages can connect to each other. We say two village A and B are connected, if and only if there is a road between A and B, or there exists a village C such that there is a road between A and C, and C and B are connected. 

We know that there are already some roads between some villages and your job is the build some roads such that all the villages are connect and the length of all the roads built is minimum.

Input

The first line is an integer N (3 <= N <= 100), which is the number of villages. Then come N lines, the i-th of which contains N integers, and the j-th of these N integers is the distance (the distance should be an integer within [1, 1000]) between village i and village j. 

Then there is an integer Q (0 <= Q <= N * (N + 1) / 2). Then come Q lines, each line contains two integers a and b (1 <= a < b <= N), which means the road between village a and village b has been built.

Output

You should output a line contains an integer, which is the length of all the roads to be built such that all the villages are connected, and this value is minimum.

Sample Input

3
0 990 692
990 0 179
692 179 0
1

/************
最小生成树：有 n个村庄，矩阵的行列不相等对应两个村庄
的距离，接下来，有两村庄已经通过的路；
数据：
输入：
3
0 990 692
990 0 179
692 179 0
1
1 2
输出：
179
***************/
#include<stdio.h>
#include<string.h>
int map[101][101];
#define Max 1001;
int prim(int n)
{
	int use[101],a[101];
	int i,j,k,sum=0;
	memset(a,0,sizeof(a));
	for(i=1;i<=n;i++)
		use[i]=map[1][i];//从第一行开始记录
	a[1]=1;
	for(i=1;i<n;i++)
	{
		int temp=Max;
		for(j=1;j<=n;j++)
		if(!a[j]&&use[j]<temp)//选择最小的开始修路
		{
			temp=use[j];
			k=j;
		}
	a[k]=1;
	sum+=use[k];
	for(j=1;j<=n;j++)//所有记录最小路
	{
		if(!a[j]&&map[k][j]<use[j])//记录通往该村的最小路
			use[j]=map[k][j];
	}
	}
	return sum;
}

int main()
{
	int n,i,j,m,x,y;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		for(j=1;j<=n;j++)
		{
			scanf("%d",&map[i][j]);
			if(!map[i][j])
				map[i][j]=Max;
		}
	scanf("%d",&m);
	for(i=0;i<m;i++)
	{
		scanf("%d%d",&x,&y);//要是已经连通我们把它们之间的距离假定为0；
		map[x][y]=map[y][x]=0;
	}
	int sum=prim( n);
	printf("%d\n",sum);
	return 0;
}

　　

1 2

Sample Output

179

Source