Eddy's picture（最小生成树）

Eddy's picture

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4113 Accepted Submission(s): 2022

Problem Description

Eddy begins to like painting pictures recently ,he is sure of himself to become a painter.Every day Eddy draws pictures in his small room, and he usually puts out his newest pictures to let his friends appreciate. but the result it can be imagined, the friends are not interested in his picture.Eddy feels very puzzled,in order to change all friends 's view to his technical of painting pictures ,so Eddy creates a problem for the his friends of you.
Problem descriptions as follows: Given you some coordinates pionts on a drawing paper, every point links with the ink with the straight line, causes all points finally to link in the same place. How many distants does your duty discover the shortest length which the ink draws?

Input

The first line contains 0 < n <= 100, the number of point. For each point, a line follows; each following line contains two real numbers indicating the (x,y) coordinates of the point.

Input contains multiple test cases. Process to the end of file.

Output

Your program prints a single real number to two decimal places: the minimum total length of ink lines that can connect all the points.

Sample Input

31.0 1.02.0 2.02.0 4.0

Sample Output

3.41

Author

eddy

题目大意：给出n个点，求出用线段连接这些点的所需的最小长度

题解：最小生成树

#include<cstdio>#include<cstring>#include<cmath>const int M=110;const double Max=999999.0;double map[M][M],cost[M];bool mark[M];int n,i,j,beg;double n1,n2,res,min;struct node{    double x,y;}p,point[M];double get_dis(node p1,node p2){    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));}using namespace std;int main(){    while(scanf("%d",&n)!=EOF)    {        for(i=1;i<=n;i++)         {             scanf("%lf%lf",&n1,&n2);             point[i].x=n1;             point[i].y=n2;         }        for(i=1;i<=n;i++)         for(j=i+1;j<=n;j++)           map[i][j]=map[j][i]=get_dis(point[i],point[j]);        memset(mark,true,sizeof(mark)),mark[1]=false;        res=0,beg=1,cost[1]=0;        for(i=1;i<=n;i++)         cost[i]=map[1][i];        j=n-1;        while(j--)        {            min=Max;            for(i=1;i<=n;++i)             if(mark[i]&&min>cost[i])              {                  min=cost[i];                  beg=i;              }            res+=min,mark[beg]=false;            for(i=1;i<=n;++i)              if(mark[i]&&cost[i]>map[beg][i])               cost[i]=map[beg][i];        }      printf("%.2lf\n",res);    }    return 0;}