[MST]POJ 1258Agri-Net

传送门：Agri-Net

Agri-Net

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 35455 Accepted: 14240

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

40 4 9 214 0 8 179 8 0 1621 17 16 0

Sample Output

28

Source

USACO 102

解题报告：

很明显的最小生成树问题。下面是三种方式。

第一种：prim 邻接矩阵

#include<iostream>#include<cstdio>#include<cstring>#define  INF   0x7fffffffusing namespace std;int a[111][111],dist[111],n;bool vis[111];int main(){    while(scanf("%d",&n)==1){        memset(vis,0,sizeof(vis));        for(int i=1;i<=n;i++)            for(int j=1;j<=n;j++){                scanf("%d",&a[i][j]);                if(a[i][j]==0)                    a[i][j]=INF;            }        for(int i=1;i<=n;i++)            dist[i]=a[1][i];        vis[1]=true;        int num=1,sum=0;        while(num<n){            int res=INF,pos;            for(int i=1;i<=n;i++)                if(dist[i]<res&&!vis[i]){                    pos=i;res=dist[i];                }            vis[pos]=true;            sum+=res;            for(int i=1;i<=n;i++)                if(!vis[i])                    dist[i]=min(dist[i],a[pos][i]);            num++;        }        printf("%d\n",sum);    }    return 0;}

第二种：prim 邻接表

#include<iostream>#include<cstdio>#include<cstring>#define  INF   0x7fffffffusing namespace std;struct edge{    int v,next,cost;}e[111*111];int ecnt,first[111];int n,v;void addedge(int u,int v,int cost){    e[++ecnt].next=first[u];    e[ecnt].v=v;    e[ecnt].cost=cost;    first[u]=ecnt;}int prim(){    bool vis[111];    int dist[111],num=1,sum=0;    memset(vis,0,sizeof(vis));    vis[1]=true;    for(int i=1;i<=n;i++)        dist[i]=INF;    for(int i=first[1];i!=-1;i=e[i].next)        dist[e[i].v]=min(dist[e[i].v],e[i].cost);    while(num<n){        int res=INF,pos;        for(int i=1;i<=n;i++)            if(dist[i]<res&&!vis[i])                pos=i,res=dist[i];        vis[pos]=true;        sum+=res;        for(int i=first[pos]; i!=-1;i=e[i].next){            int v=e[i].v;            if(vis[v]) continue;            dist[v] = min(dist[v], e[i].cost);        }        num++;    }    return sum;}int main(){    while(scanf("%d",&n)==1){        memset(first,-1,sizeof(first));        ecnt=-1;        for(int i=1;i<=n;i++)            for(int j=1;j<=n;j++){                scanf("%d",&v);                if(v!=0)                    addedge(i,j,v);            }        printf("%d\n",prim());    }    return 0;}

第三种：kruscal

#include<iostream>#include<cstdio>#include<algorithm>using namespace std;struct edge{    int v,u,cost;}e[111*111];bool cmp(const edge &a,const edge &b){    return a.cost<b.cost;}int ecnt,fa[111],n,v;void addedge(int u,int v,int cost){    e[++ecnt].v = v;    e[ecnt].u = u;    e[ecnt].cost = cost;}int getf(int x){    return fa[x]==x?x:fa[x]=getf(fa[x]);}int kruscal(){    int sum=0;    for(int i=1;i<=n;i++)        fa[i]=i;    sort(e+1,e+1+ecnt,cmp);    for(int i=1;i<=ecnt;i++){        int u=e[i].u,v=e[i].v;        u=getf(u);        v=getf(v);        if(u==v) continue;        sum+=e[i].cost;        fa[u]=v;    }    return sum;}int main(){    while(scanf("%d",&n)==1){        ecnt=0;        for(int i=1;i<=n;i++)            for(int j=1;j<=n;j++){                scanf("%d",&v);                if(v!=0)                    addedge(i,j,v);            }        printf("%d\n",kruscal());    }    return 0;}