Comet OJ

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_xsum_{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;
}