poj 2421 Constructing Roads（最小生成树）

最新推荐文章于 2023-07-12 10:30:50 发布

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本文探讨了一种算法解决方案，用于确定如何在已存在的部分连接的村庄间构建最小总长度的道路网络，确保所有村庄都能互相连接。该问题通过寻找剩余未连接村庄间的最小生成树来解决。

Constructing Roads

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 22124		Accepted: 9431

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

Sample Output

题意：给一个初始图，再给 m条边，a,b表明a和b不需要花费时间可以直接到达，问最小生成树是多少

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
#define N 150
#define INF 99999999
int ma[N][N];
long long d[N],vis[N];
int n;
long long prim(int s)
{
    for(int i=1; i<=n; i++)
        d[i]=i==s?0:ma[s][i];
    vis[s]=1;
    long long ans=0;
    for(int i=1; i<n; i++)
    {
        int maxn=INF,v;
        for(int j=1; j<=n; j++)
            if(!vis[j]&&maxn>d[j])
            {
                maxn=d[j];
                v=j;
            }
        vis[v]=1;
        ans+=maxn;
        for(int j=1; j<=n; j++)
            if(!vis[j]&&ma[v][j]<d[j])
                d[j]=ma[v][j];
    }
    return ans;
}
int main()
{
    int m;
    int s,e;
    while(~scanf("%d",&n))
    {
        memset(vis,0,sizeof(vis));
        for(int i=1; i<=n; i++)
            for(int j=1; j<=n; j++)
                scanf("%d",&ma[i][j]);
        scanf("%d",&m);
        while(m--)
        {
            scanf("%d %d",&s,&e);
            ma[s][e]=0;
            ma[e][s]=0;
        }
        long long ans=prim(1);
        printf("%lld\n",ans);
    }
    return 0;
}