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  • SHUOJ 241 Franklin's Trouble(简单数学题)

    http://acmoj.shu.edu.cn/openjudge/viewproblem?coll_id=1&prob_id=241

    Franklin's Trouble

    Description

    Professor Franklin is consulting for an oil company, which is planning a large pipeline running east to west through an oil field of M wells. From each well, a sub-pipeline is to be connected directly to the main pipeline along a shortest path (either north or south). Given x- and y-coordinates of the wells, the professor wants to pick the optimal location of the main pipeline, which means to minimize the total length of the sub-pipelines. Franklin is not good at calculation, but you are. Can you help him?

    Input

    The first line of input contains a single integer N representing the number of oil fields. Then N field descriptions follow. Each field description starts with an integer M representing the number of wells in this field. Each well is represented by a point (x, y) (both x and y are integers). You can assume all integers are between 1 and 100 and no two wells share the same x-coordinate.

    Output

    For each field, output the total length of the sub-pipelines. The length should be minimized.

    Sample Input

    1

    2

    1 0

    2 1

    Sample Output

    1

    Explanation

    In sample input, there is only one case. In this case, the main pipeline can be located at any position between y=0 and y=1 lines to reach the optimal result 1.

    题目意思就是M个点,求一条水平线,使得所有点到水平线的距离之和最小。输出最小距离之和

    输入数据的X坐标不相等。

    很简单的数学题,明显应该选在Y坐标的中位数处,可以使得距离之和最小;;

    #include<stdio.h>
    #include<algorithm>
    using namespace std;
    const int MAXN=1000;
    int y[MAXN];
    int main()
    {
        int T;
        int n;
        int x;
        scanf("%d",&T);
        while(T--)
        {
            scanf("%d",&n);
            for(int i=0;i<n;i++)
              scanf("%d%d",&x,&y[i]);
            sort(y,y+n);
            int tmp=y[n/2];
            int res=0;
            for(int i=0;i<n;i++)
              res+=abs(tmp-y[i]);
            printf("%d\n",res);
        }    
        return 0;
    }    
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  • 原文地址:https://www.cnblogs.com/kuangbin/p/2490610.html
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