（最小树形图朱刘算法） poj 3164-优快云博客

文章介绍了一种在紧急情况下快速构建通信网络的方法。通过寻找最短路径并避免形成闭环来确保资源消耗最少，同时保证每个节点都能接收到指令。

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Command Network

Time Limit: 1000MS		Memory Limit: 131072K
Total Submissions: 14340		Accepted: 4118

Description

After a long lasting war on words, a war on arms finally breaks out between littleken’s and KnuthOcean’s kingdoms. A sudden and violent assault by KnuthOcean’s force has rendered a total failure of littleken’s command network. A provisional network must be built immediately. littleken orders snoopy to take charge of the project.

With the situation studied to every detail, snoopy believes that the most urgent point is to enable littenken’s commands to reach every disconnected node in the destroyed network and decides on a plan to build a unidirectional communication network. The nodes are distributed on a plane. If littleken’s commands are to be able to be delivered directly from a node A to another node B, a wire will have to be built along the straight line segment connecting the two nodes. Since it’s in wartime, not between all pairs of nodes can wires be built. snoopy wants the plan to require the shortest total length of wires so that the construction can be done very soon.

Input

The input contains several test cases. Each test case starts with a line containing two integer N (N ≤ 100), the number of nodes in the destroyed network, and M (M ≤ 10⁴), the number of pairs of nodes between which a wire can be built. The next N lines each contain an ordered pair x_i and y_i, giving the Cartesian coordinates of the nodes. Then follow M lines each containing two integers i and j between 1 and N (inclusive) meaning a wire can be built between node i and node j for unidirectional command delivery from the former to the latter. littleken’s headquarter is always located at node 1. Process to end of file.

Output

For each test case, output exactly one line containing the shortest total length of wires to two digits past the decimal point. In the cases that such a network does not exist, just output ‘poor snoopy’.

Sample Input

Sample Output

31.19
poor snoopy

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<limits.h>
using namespace std;
const int MAXN = 110;
const int MAXM = 10010;

struct node
{
    int from;
    int to;
    double w;
};
node e[MAXM];

struct node1
{
    double x;
    double y;
};
node1 Point[MAXN];

double Dist(node1 a, node1 b)
{
    double x=a.x-b.x;
    double y=a.y-b.y;
    return sqrt(x*x+y*y);
}

int pre[MAXN],vis[MAXN],flag[MAXN];
double In[MAXN],sum;

double ZhuLiu(int root,int N,int M)
{
    sum=0;
    while(true)
    {
        for(int i=0;i<N;++i)
            In[i]=INT_MAX;
        for(int i=0;i<M;++i)
        {
            int u=e[i].from;
            int v=e[i].to;
            if(e[i].w<In[v]&&u!= v)
            {
                pre[v]=u;//v为终点，pre[v]存放起点
                In[v]=e[i].w;//权值最小的边
            }
        }

        for(int i=0;i<N;++i)//如果存在除root以外的孤立点，则不存在最小树形图
        {
            if(i==root)
                continue;
            if(In[i]==INT_MAX)
                return -1;
        }
        int CntNode=0;
        memset(flag,-1,sizeof(flag));
        memset(vis,-1,sizeof(vis));
        In[root]=0;
        for(int i=0;i<N;++i)   //找环,标记每个环
        {
            sum+=In[i];
            int v=i;
            while(vis[v]!=i&&flag[v]==-1&&v!=root)//每个点寻找其前序点，要么最终寻找至根部，要么找到一个环
            {
                vis[v]=i;
                v=pre[v];
            }
            if(v!=root&&flag[v]==-1)  //新图重新编号
            {
                for(int u=pre[v];u!=v;u=pre[u])
                    flag[u]=CntNode;
                flag[v]=CntNode++;
            }
        }
        if(CntNode==0)    //无环，跳出
            break;
        for(int i=0;i<N;++i)
        {
            if(flag[i]==-1)
                flag[i]=CntNode++;
        }
        for(int i=0;i<M;++i)  //建立新图，更新其他点到环的距离
        {
            int v=e[i].to;
            e[i].from=flag[e[i].from];
            e[i].to=flag[e[i].to];
            if(e[i].from!=e[i].to)
                e[i].w-=In[v];
        }
        N=CntNode;
        root=flag[root];
    }
    return sum;
}

int main()
{
    int x,y,N,M;
    while(~scanf("%d%d",&N,&M))
    {
        int id=0;
        for(int i=0;i< N;++i)
            scanf("%lf%lf",&Point[i].x,&Point[i].y);
        for(int i=0;i<M;++i)
        {
            scanf("%d%d",&x,&y);
            if(x==y)
                continue;
            x--;
            y--;
            e[id].from=x;
            e[id].to=y;
            e[id++].w=Dist(Point[x],Point[y]);
        }
        double ans=ZhuLiu(0,N,id);
        if(ans==-1)
            printf("poor snoopy\n");
        else
            printf("%.2f\n",ans);
    }
    return 0;
}

转载于:https://www.cnblogs.com/water-full/p/4485900.html