POJ 1258 Agri-Net（最小生成树）

最新推荐文章于 2019-08-24 23:34:37 发布

转载最新推荐文章于 2019-08-24 23:34:37 发布 · 73 阅读

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原文链接：http://www.cnblogs.com/sola1994/p/4134873.html

本文通过解决农民约翰为实现竞选承诺而面临的连接各农场互联网的问题，介绍了如何使用Kruskal和Prim算法找到连接所有节点所需的最小生成树。文章提供了详细的代码实现，并对比了两种算法的特点。

Agri-Net

Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u

Submit Status Practice POJ 1258

Description

Farmer John has been elected mayor of his town! One of his campaign promises was to bring internet connectivity to all farms in the area. He needs your help, of course.
Farmer John ordered a high speed connection for his farm and is going to share his connectivity with the other farmers. To minimize cost, he wants to lay the minimum amount of optical fiber to connect his farm to all the other farms.
Given a list of how much fiber it takes to connect each pair of farms, you must find the minimum amount of fiber needed to connect them all together. Each farm must connect to some other farm such that a packet can flow from any one farm to any other farm.
The distance between any two farms will not exceed 100,000.

Input

The input includes several cases. For each case, the first line contains the number of farms, N (3 <= N <= 100). The following lines contain the N x N conectivity matrix, where each element shows the distance from on farm to another. Logically, they are N lines of N space-separated integers. Physically, they are limited in length to 80 characters, so some lines continue onto others. Of course, the diagonal will be 0, since the distance from farm i to itself is not interesting for this problem.

Output

For each case, output a single integer length that is the sum of the minimum length of fiber required to connect the entire set of farms.

Sample Input

Sample Output

28

裸最小生成树 可以用kruskal和prim来完成

kruskal

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
int n,coun;
struct road
{
    int f,t;
    int w;
};
road vil[10000+10];
int fa[10000+10];
int cmp(road a ,road b) {return a.w<b.w;}
int find(int x)
{
    return fa[x]==x?x:fa[x]=find(fa[x]);
}
int Kruskal()
{
    int ans=0;
    for(int i=0;i<coun;i++) fa[i]=i;
    sort(vil,vil+coun,cmp);
    for(int i=0;i<coun;i++)
    {
        int x=find(vil[i].f);
        int y=find(vil[i].t);
        if(x!=y)
        {
            fa[x]=y;
            ans+=vil[i].w;
        }
    }
    return ans;
}
int main()
{

    int i,j;
    while(scanf("%d",&n)!=EOF)
    {
        coun=0;
        for(i=1;i<=n;i++)
        {
            for(j=1;j<=n;j++)
            {
                int waste;
                scanf("%d",&waste);
                if(i<j)
                {
                    vil[coun].f=i;
                    vil[coun].t=j;
                    vil[coun].w=waste;
                    coun++;
                }
            }
        }
        int ans=Kruskal();
        printf("%d\n",ans);
    }
    return  0;
}

View Code

prim

（网上贴来的代码感觉明显kruskal比较简单粗暴啊）

#include<iostream>
using namespace std;

const int inf=100001;      //无限大

int n;   //农场数量
int dist[101][101];

int prim(void)
{
    int s=1;
    int m=1;
    bool u[101]={false};
    u[s]=true;

    int min_w;
    int prim_w=0;
    int point;
    int low_dis[101];

    /*Initial*/

    for(int i=1;i<=n;i++)
        low_dis[i]=inf;

    /*Prim Algorithm*/

    while(true)
    {
        if(m==n)
            break;
        min_w=inf;
        for(int i=2;i<=n;i++)
        {
            if(!u[i] && low_dis[i]>dist[s][i])
                low_dis[i] = dist[s][i];
            if(!u[i] && min_w>low_dis[i])
            {
                min_w = low_dis[i];
                point=i;
            }
        }
        s=point;
        u[s]=true;
        prim_w+=min_w;
        m++;
    }
    return prim_w;
}

int main(void)
{
    while(cin>>n)
    {
        /*Input*/

        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
                cin>>dist[i][j];

        /*Prim Algorithm & Output*/

        cout<<prim()<<endl;
    }
    return 0;
}