HackerRank Week of Code 31Colliding Circles

Posted 2020-11-20 abclzr

https://www.hackerrank.com/contests/w31/challenges/colliding-circles/problem
设E(n)为序列长度为n时的期望值。
[ egin{aligned} E(n-1)=&E(n)+frac1{nchoose2}sum_{0leq i<jleq n}2r_ir_j=&E(n)+frac1{nchoose2}left[left(sum r_i ight)^2-sum r_i^2 ight]\=&E(n)+frac1{nchoose2}left[left(sum r_i ight)^2-E(n) ight]\end{aligned} ]
(O(n))递推。

#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int N = 100003;

double a[N], sum = 0, E[N];
int n, k;

int main() {
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= n; ++i) scanf("%lf", &a[i]), sum += a[i], E[n] += a[i] * a[i];
    
    for (int i = 1; i <= k; ++i) {
        E[n - 1] = (1.0 - (2.0 / n / (n - 1))) * E[n] + sum * sum * 2 / n / (n - 1);
        --n;
    }
    
    printf("%.10lf
", E[n] * acos(-1));
    
    return 0;
}