UVA 10041 Vito's Family (中位数)

 

Problem C: Vito's family

 

 

Background 

The world-known gangster Vito Deadstone is moving to New York. He has a very big family there, all of them living in Lamafia Avenue. Since he will visit all his relatives very often, he is trying to find a house close to them.

 

Problem 

Vito wants to minimize the total distance to all of them and has blackmailed you to write a program that solves his problem.

 

Input 

The input consists of several test cases. The first line contains the number of test cases.

For each test case you will be given the integer number of relatives r ( 0 < r < 500) and the street numbers (also integers) where they live ( 0 < s_i < 30000 ). Note that several relatives could live in the same street number.

 

Output 

For each test case your program must write the minimal sum of distances from the optimal Vito's house to each one of his relatives. The distance between two street numbers  s _i  and  s _j  is  d _ij = | s _i - s _j |.

 

Sample Input 

2

2 2 4 

3 2 4 6

Sample Output 

2

4

题意：Vito有r个邻居。。在一条街道上。每个邻居有一个位置。 要求出Vito住的一个地方使得他到所有邻居距离总和最短。

思路：求中位数。。其实也不用求到中位数。。只要把所有邻居从小到大排序，分成两边。取最中间数就可以了。如果是偶数。就两个随便取一个就可以了。。具体原因自己想。

代码：

 

#include <stdio.h>

#include <string.h>

#include <ctype.h>

#include <algorithm>

using namespace std;



int t, r, s[505], mid, sum;



int main() {

    scanf("%d", &t);

    while (t --) {

	sum = 0;

	scanf("%d", &r);

	for (int i = 0; i < r; i ++)

	    scanf("%d", &s[i]);

	sort(s, s + r);

	mid = s[r / 2];

	for (int i = 0; i < r ; i ++) {

	    sum += abs(s[i] - mid);

	}

	printf("%d\n", sum);

    }

    return 0;

}