HDU 1102 Constructing Roads（Prim算法）

Constructing Roads

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 20793    Accepted Submission(s): 7944

Problem 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

30 990 692990 0 179692 179 011 2

 

Sample Output

179

 

本题题中直接给出了邻接矩阵，比较方便。对于已经建设道路的村庄，可以直接把他们之间的距离设置为0。

下面附上AC代码：

#include<iostream>
#include<cstdio>
#include<string.h>
using namespace std;
int map[1001][1001];
int dist[1001];
int visited[1001];
int n,sum;
const int inf=9999999;


void Prim()
{
    sum=0;
    memset(visited,0,sizeof(visited));
    visited[1]=1;
    for(int i=1;i<=n;i++)
        dist[i]=map[1][i];
    for(int i=1;i<n;i++)
    {
        int min=inf;
        int pos;
        for(int j=1;j<=n;j++)
        {
            if(!visited[j]&&min>dist[j])
            {
                min=dist[j];
                pos=j;
            }
        }
        if(min>=inf) break;
        visited[pos]=1;
        sum+=min;
        for(int j=1;j<=n;j++)
        {
            if(!visited[j]&&dist[j]>map[pos][j])
                dist[j]=map[pos][j];
        }


    }
}
int main()
{
    while(cin>>n)
    {
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
                cin>>map[i][j];
        int q;
        cin>>q;
        while(q--)
        {
            int a,b;
            cin>>a>>b;
            map[a][b]=0;
            map[b][a]=0;
        }
        Prim();
        cout<<sum<<endl;
    }
    return 0;
}