牛客IOI周赛23-提高组 星星 （环形均分纸牌问题）

题面

题解

1. 环形均分纸牌问题：详细的点这里，

2. 主要思想：我们看作是单向传递，可以由公式推导出 c[i] = s[i - 1] - (i - 1) * avg;
   数组c就是仓库选址的c，中位数就是最优解

代码

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

using namespace std;
typedef long long ll;
const int N = 1e6 + 10;

int n;
ll a[N], s[N], c[N];

ll slove() {
    
    

    for (int i = 1; i <= n; i++) s[i] = s[i - 1] + a[i];

    ll avg = s[n] / n;

    c[1] = 0;
    for (int i = 2; i <= n; i++) c[i] = s[i - 1] - (i - 1) * avg;

    sort(c + 1, c + 1 + n);

    ll res = 0;
    for (int i = 1; i <= n; i++) res += abs(c[i] - c[(n + 1) / 2]);

    return res;

}


int main() {
    
    

    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];

    cout << slove() << endl;

    return 0;
}