Educational Codeforces Round 3 609C Load Balancing(脑洞)

C. Load Balancing

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

In the school computer room there are n servers which are responsible for processing several computing tasks. You know the number of scheduled tasks for each server: there are mi tasks assigned to the i-th server.

In order to balance the load for each server, you want to reassign some tasks to make the difference between the most loaded server and the least loaded server as small as possible. In other words you want to minimize expression ma - mb, where a is the most loaded server and b is the least loaded one.

In one second you can reassign a single task. Thus in one second you can choose any pair of servers and move a single task from one server to another.

Write a program to find the minimum number of seconds needed to balance the load of servers.

Input

The first line contains positive number n (1 ≤ n ≤ 105) — the number of the servers.

The second line contains the sequence of non-negative integers m1, m2, ..., mn (0 ≤ mi ≤ 2·104), where mi is the number of tasks assigned to the i-th server.

Output

Print the minimum number of seconds required to balance the load.

Sample test(s)

input

2
1 6

output

2

input

7
10 11 10 11 10 11 11

output

0

input

5
1 2 3 4 5

output

3

Note

In the first example two seconds are needed. In each second, a single task from server #2 should be moved to server #1. After two seconds there should be 3 tasks on server #1 and 4 tasks on server #2.

In the second example the load is already balanced.

A possible sequence of task movements for the third example is:

1. move a task from server #4 to server #1 (the sequence m becomes: 2 2 3 3 5);
2. then move task from server #5 to server #1 (the sequence m becomes: 3 2 3 3 4);
3. then move task from server #5 to server #2 (the sequence m becomes: 3 3 3 3 3).

The above sequence is one of several possible ways to balance the load of servers in three seconds.

题目链接:点击打开链接

n台服务, 任意一台服务器可在一秒内将自己任务减一转移给其他服务器, 问几秒后可以使得max - min最小.

由大到小对任务量进行排序, 考虑任务合sum是否可以整除n, 若可以整除, 直接计算与平均数的差值即可. 否则, 多出来的数要计算与

(ave + 1)的差值, 因为这些大的任务与最小任务差值必然为1, 其他数计算与ave的差值.

AC代码:

#include "iostream"
#include "cstdio"
#include "cstring"
#include "algorithm"
#include "queue"
#include "stack"
#include "cmath"
#include "utility"
#include "map"
#include "set"
#include "vector"
#include "list"
#include "string"
#include "cstdlib"
using namespace std;
typedef long long ll;
const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int MAXN = 1e5 + 5;
int n, a[MAXN], sum, ans;
bool cmp(int a, int b)
{
    return a > b;
}
int main(int argc, char const *argv[])
{
    scanf("%d", &n);
    for(int i = 0; i < n; ++i) {
        scanf("%d", &a[i]);
        sum += a[i];
    }
    sort(a, a + n, cmp);
    int ave = sum / n;
    if(sum % n) {
        for(int i = 0; i < sum % n; ++i)
            if(a[i] >= ave + 1) ans += a[i] - (ave + 1);
        for(int i = sum % n; i < n; ++i)
            if(a[i] >= ave) ans += a[i] - ave;
    }
    else {
        for(int i = 0; i < n; ++i)
            if(a[i] > ave) ans += a[i] - ave;
            else break;
    }
    printf("%d\n", ans);
    return 0;
}