题解 | #Little Pony and Expected Maximum#

【Little Pony and Expected Maximum】

定义$P(Y=y)P(Y=y)$为投$nn$次，得到最大点数为$yy$的概率，但是这个值直接计算比较难。

可以先定义$P(Y\le y)P(Y\backslash le\; y)$为最大点数小于$yy$的概率，则$P(Y=y)=P(Y\le y)-P(Y\le y-1)P(Y=y)=P(Y\backslash le\; y)-P(Y\backslash le\; y-1)$

期望为:

#include <bits/stdc++.h>
using namespace std;

double power(double a, int b) {
    double res = 1.0;
    while (b) {
        if (b & 1) res = res * a;
        b >>= 1;
        a = a * a;
    }
    return res;
}
int n, m;
int main() {
    cin >> m >> n;
    double res = 0;
    for (int i = 1; i <= m; i++)
        res += i * (power(1.0 * i / m, n) - power(1.0 * (i - 1) / m, n));
    printf("%.12lf", res);
    return 0;
}