"Explanations" Luo Valley P4016 load balancing

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Problem Portal

Portal1: Luogu

Portal2: LibreOJ

Description

\ (G \) company \ (n-\) th line arranged along the annular rail transport warehouse, varying amounts of goods stored in each warehouse. How can you make with the least amount of handling \ (n \) the same number of warehouse inventory. When handling cargo, handling only between adjacent warehouse.

Input

The first file \ (1 \) line there \ (1 \) positive integers \ (n \) , expressed \ (n \) warehouse.

The first \ (2 \) line there \ (n \) positive integer representing \ (n \) inventory depots.

Output

Conveying the least amount of output.

Sample Input

5
17 9 14 16 4

Sample Output

11

Hint

For \ (100 \% \) test data: \ (. 1 \ n-Leq \ Leq 100 \) .

Solution

Although the network flow 24problem, in fact, greedy + Sort enough.

Code

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>

using namespace std;

const int MAXN=105;
int n, a[MAXN]; 
int main() {
    scanf("%d",&n);
    int sum=0;
    for (int i=1; i<=n; i++) {
        scanf("%d",&a[i]);
        sum+=a[i];
    }
    sum/=n;
    for (int i=1; i<=n; i++)
        a[i]+=a[i-1]-sum;
    sort(a+1, a+n+1);
    sum=a[(n+1)>>1];//尽量用位运算，比较快
    int ans=0;
    for (int i=1; i<=n; i++)
        ans+=abs(a[i]-sum);//计算每一个距离中间的位置
    printf("%d\n",ans);
    return 0;
}

Attachment

Test data Download: https://www.lanzous.com/i3juukh