POJ1258 Agri-Net——————最小生成树

ゝ一纸荒年。 2022-05-16 06:28 72阅读 0赞

**Agri-Net**

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    <div>
      Agri-Net 
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        <td><b>Time Limit:</b> 1000MS</td> 
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        <td><b>Memory Limit:</b> 10000K</td> 
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        <td><b>Total Submissions:</b> 68143</td> 
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        <td><b>Accepted:</b> 28244</td> 
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    </div><p>Description</p> 
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      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. 
     <br>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. 
     <br>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. 
     <br>The distance between any two farms will not exceed 100,000. 
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    </div><p>Input</p> 
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      The input includes several cases. For each case, the first line contains the number of farms, N (3 &lt;= N &lt;= 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. 
    </div><p>Output</p> 
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      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. 
    </div><p>Sample Input</p><pre>4
0 4 9 21
4 0 8 17
9 8 0 16
21 17 16 0
</pre><p>Sample Output</p><pre>28</pre><p>Source</p> 
    <div> 
     <a rel="nofollow">USACO 102</a> 
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给的是点与点之间的邻接矩阵  
求这些点的最小生成树

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//#include<bits/stdc++.h>
    #include<cstdio>
    #include<vector>
    #include<algorithm>
    
    using namespace std;
    const int MAXN=505;
    int n,m,pre[MAXN];
    struct Edge{
        int x,y,dis;
        Edge(){}
        Edge(int x1,int y1,int dis1)
        {
            x=x1; y=y1; dis=dis1;
        }
    };
    bool cmp(Edge a,Edge b)
    {
        return a.dis<b.dis;
    }
    vector<Edge>d;
    void init(){
       for(int i=1;i<=n;i++) pre[i]=i; }
    int find(int x){
       return pre[x]==x?x:pre[x]=find(pre[x]); }
    bool join(int x,int y)
    {
        x=find(x);
        y=find(y);
        if(x!=y)
        {
            pre[x]=y;
            return true;
        }
        return false;
    }
    
    
    int main()
    {
    
        while(~scanf("%d",&n))
        {
            d.clear();
            init();
            for(int i=1;i<=n;i++)
                for(int j=1;j<=n;j++)
                {
                    int x;
                    scanf("%d",&x);
                    if(i==j)    continue;
                    d.push_back(Edge(i,j,x));
                }
            sort(d.begin(),d.end(),cmp);
            int cnt=0,ans=0;
            for(int i=0;i<d.size();i++)
            {
                Edge e=d[i];
                if(join(e.x,e.y))
                {
                    cnt++;
                    ans+=e.dis;
                }
                if(cnt==n-1) break;
            }
            printf("%d\n",ans);
        }
        return 0;
    }