[中位数]A mid-summer night's dream.uva10057

Problem C

A mid-summer night’s dream

Input: standard input

Output: standard output

 

This is year 2200AD. Science has progressed a lot in two hundred years. Two hundred years is mentioned here because this problem is being sent back to 2000AD with the help of time machine. Now it is possible to establish direct connection between man and computer CPU. People can watch other people’s dream on 3D displayer (That is the monitor today) as if they were watching a movie. One problem in this century is that people have become so dependent on computers that their analytical ability is approaching zero. Computers can now read problems and solve them automatically. But they can solve only difficult problems. There are no easy problems now. Our chief scientist is in great trouble as he has forgotten the number of his combination lock. For security reasons computers today cannot solve combination lock related problems. In a mid-summer night the scientist has a dream where he sees a lot of unsigned integer numbers flying around. He records them with the help of his computer, Then he has a clue that if the numbers are (X1, X2,   …  , Xn) he will have to find an integer number A (This A is the combination lock code) such that

             

             (|X1-A| + |X2-A| + … … + |Xn-A|) is minimum.

 

Input

Input will contain several blocks. Each block will start with a number n (0<n<=1000000) indicating how many numbers he saw in the dream. Next there will be n numbers. All the numbers will be less than 65536. The input will be terminated by end of file.

 

Output

For each set of input there will be one line of output. That line will contain the minimum possible value for A. Next it will contain how many numbers are there in the input that satisfy the property of A (The summation of absolute deviation from A is minimum). And finally you have to print how many possible different integer values are there for A (these values need not be present in the input). These numbers will be separated by single space.

 

Sample Input:

2
10
10
4
1
2
2
4

Sample Output:

10 2 1
2 2 1

______________________________________________________________________________________________Shahriar Manzoor
16-12-2000

题意：我们的科学领导人遇到一个很大的问题，他忘掉了他的密码锁的号码，基于安全性考量，目前的电脑无法解决密码锁的问题。在一个仲夏夜里，科学家做了一个梦，梦里他看到许多数字飞来飞去。他把这些数字纪录在电脑上。接着他想到有一个线索，假如数字列为（X ₁ , X ₂ , … , X _n）他必须找到一个整数A（A就是他密码锁的密码）使得（ |X ₁-A| + |X ₂ -A| + … … + |X _n -A|）为最小。

思路：很容易就能看出来这个数就是这个数组的中位数。只需区分偶数和奇数的情况就可以了。

数学都忘光了。这个都差点给忘了。。

#include<iostream>#include<algorithm>using namespace std;int arry[1000005];int n;int main(){    while(cin>>n)    {        int i,j,k;        for(i=0;i<n;i++)            cin>>arry[i];        sort(arry,arry+n);        int minc,maxc,num=0,sum=0;        if(n%2)        {            sum=1;            minc=arry[n/2];            maxc=arry[n/2];        }        else        {            sum=arry[n/2]-arry[n/2-1]+1;            minc=arry[n/2-1];            maxc=arry[n/2];        }        for(i=0;i<n;i++)        {            if(arry[i]>=minc&&arry[i]<=maxc) num++;            if(arry[i]>maxc) break;        }        cout<<minc<<" "<<num<<" "<<sum<<endl;    }    return 0;}