Comet OJ - Contest #8 B [支援城市]

Comet OJ - Contest #8 B 支援城市

直接模拟 \(O(n^2)\) TLE ，把式子展开计算，\(O(n)\)

\[\sum_{i = 1}^n {(w_i - w_x)^2} = \sum_{i = 1}^n(w_i^2 - 2w_iw_x + w_x^2) = \sum_{i = 1}^n w_i^2 - 2w_x\sum_{i = 1}^n w_i + \sum_{i = 1}^n w_x^2 \]

将 $ \sum_{i = 1}^n w_i^2$ 记作 \(ss\)

将 \(\sum_{i = 1}^n w_i\) 记作 \(s\)

上述表达式简写成 ： $ ss - 2w_xs + nw_x^2$

代码

#include <iostream>
using namespace std;
const int N = 1e5 + 10;
typedef long long ll;
ll a[N],s,ss;
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0),cout.tie(0);
	int n;
	cin >> n;
	for(int i = 0;i < n; ++i){
		cin >> a[i];
		s += a[i];
		ss += a[i] * a[i];
	}
	for(int i = 0;i < n; ++i){
		cout << ss - 2 * a[i] * s + n * a[i] * a[i] <<' ';
	}
	return 0;
}