CodeForces 453A 概率題
Description
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the
m
Input
A single line contains two integers m
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn‘t exceed 10??-?4.
Sample Input
Input6 1Output
3.500000000000Input
6 3Output
4.958333333333Input
2 2Output
1.750000000000
Hint
Consider the third test example. If you‘ve made two tosses:
- You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
- You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
- You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
- You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
#include<iostream> //此題要先轉化成概率形式,否則會爆double的 #include<cstdio> #include<cmath> #include<cstring> #include<queue> #include<algorithm> #define INF 0x3f3f3f3f using namespace std; int a[200010]; int main() { int n, m; while(~scanf("%d%d", &m, &n)) { double ans = 0; for (int i = 1; i < m; i++) ans += pow((double)i / m, n); printf("%.12lf\n", (double) m - ans); } } /* #include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<queue> #include<algorithm> #define INF 0x3f3f3f3f using namespace std; int a[200010]; int main() { int n,m; while(~scanf("%d%d",&m,&n)) { double sum1=0,sum2=0,sum=0; for(int i=1;i<=m;i++) { sum2=pow(i*1.0/m,n); sum+=i*(sum2-sum1); sum1=sum2; } double ss=1.0*sum; printf("%.12lf\n",ss); } } */
CodeForces 453A 概率題