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1037B--Reach Median(中位數)

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median 中位數 odd 奇數 even 奇數

You are given an array aa of nn integers and an integer ss. It is guaranteed that nn is odd.

In one operation you can either increase or decrease any single element by one. Calculate the minimum number of operations required to make the median of the array being equal to

ss.

The median of the array with odd length is the value of the element which is located on the middle position after the array is sorted. For example, the median of the array 6,5,86,5,8 is equal to 66, since if we sort this array we will get 5,6,85,6,8, and 66 is located on the middle position.

Input

The first line contains two integers

nn and ss (1n2?105?11≤n≤2?105?1, 1s1091≤s≤109) — the length of the array and the required value of median.

The second line contains nn integers a1,a2,,ana1,a2,…,an (1ai1091≤ai≤109) — the elements of the array aa.

It is guaranteed that nn is odd.

Output

In a single line output the minimum number of operations to make the median being equal to

ss.

Examples input Copy
3 8
6 5 8
output Copy
2
input Copy
7 20
21 15 12 11 20 19 12
output Copy
6
Note

In the first sample, 66 can be increased twice. The array will transform to 8,5,88,5,8, which becomes 5,8,85,8,8 after sorting, hence the median is equal to 88.

In the second sample, 1919 can be increased once and 1515 can be increased five times. The array will become equal to 21,20,12,11,20,20,1221,20,12,11,20,20,12. If we sort this array we get 11,12,12,20,20,20,2111,12,12,20,20,20,21, this way the median is 2020.

題意:給你一個含有n個數字的數組,問改動多少次才能使這個數組的中位數為s,每次改動只能使一個數字加1或減1

分析:先給這個數組從低到高排序,找出其中的中位數,從後面到中位數的位置遍歷,即(n to n/2+1),判斷,如果其中有數字小於s,則改動次數加上s-a[i],當i等於n/2+1時,判斷,如果大於了s,改動次數加上a[i]-s;再從(1 to n/2)遍歷,如果有a[i]>s,改動次數加上a[i]-s.

總之,要使中位數之前的都小於等於中位數,中位數之後的都大於等於中位數。

 1 #include<cstdio>
 2 #include<algorithm>
 3 using namespace std;
 4 int main()
 5 {
 6     long long n,s,a[200005];
 7     while(~scanf("%lld %lld",&n,&s))
 8     {
 9         for(int i=1;i<=n;i++)
10             scanf("%lld",&a[i]);
11         sort(a+1,a+1+n);
12         long long sum=0;
13         for(int i=n;i>=n/2+1;i--)
14         {
15             if(a[i]<s)
16                 sum+=s-a[i];
17             if(i==n/2+1&&a[i]>s)
18                 sum+=a[i]-s;
19         }
20         for(int i=n/2;i>=1;i--)
21         {
22             if(a[i]>s)
23                 sum+=a[i]-s;
24         }
25         printf("%lld\n",sum);
26     }
27     return 0;
28 }

1037B--Reach Median(中位數)