HDU 5734 Acperience (公式推导) 2016杭电多校联合第二场

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
using namespace std;
int gcd(long long a,long long b)
{
    if(!b) return a;
    return gcd(b,a%b);
}
int a[100005];
int main() {
    int T,n;
    scanf("%d",&T);
    while(T--) {
        long long sum=0;
        scanf("%d",&n);
        for(int i=0;i<n;i++) {
            scanf("%d",&a[i]);
            if(a[i]<0) a[i] = -a[i];
            sum+=a[i];
        }
        long long ap = sum,aq = n;
        long long g = gcd(n,sum);
        ap = ap/g;
        aq = aq/g;
        //printf("%I64d/%I64d\n",ap,aq);
        long long z=0;
        long long m=0;
        for(int i=0;i<n;i++) {
            z+=a[i]*a[i];
            m+=2*a[i];
        }
        long long p,q;
        //p = ap*ap*n;
        //q = aq*aq;
        p = n*z-sum*sum;
        q = n;
        g = gcd(q,p);
        p /= g;
        q /= g;

        printf("%I64d/%I64d\n",p,q);
    }
}