A. Little Pony and Expected Maximum
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-th
face contains mdots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability .
Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
A single line contains two integers m and n (1 ≤ m, n ≤ 105).
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.
6 1
3.500000000000
6 3
4.958333333333
2 2
1.750000000000
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:
这里先推出每个数是当前序列的最大值的概率,一直推不出来,后来看了别人的思路懂了,最大值不超过i的所有序列总数是i^n,但是其中含有最大值不是i的序列,比如都是1,所以要减去最大值不超过i-1的所有序列的总数,最后结果是i^n-(i-1)^n;然后因为数字太大,所以每个都先除以m^n后再算。
#include<stdio.h>
#include<math.h>
int main()
{
int n,m;double sum;
scanf("%d%d",&m,&n);
sum=m;
for(int i=1;i<m;i++)
{
sum-=pow((double)1.0-(double)i/m,(double)n);
}
printf("%.12lf\n",sum);
return 0;
}
A. Little Pony and Expected Maximum的更多相关文章
- CodeForces 454C Little Pony and Expected Maximum
Little Pony and Expected Maximum Time Limit:1000MS Memory Limit:262144KB 64bit IO Format:%I6 ...
- Codeforces Round #259 (Div. 2) C - Little Pony and Expected Maximum (数学期望)
题目链接 题意 : 一个m面的骰子,掷n次,问得到最大值的期望. 思路 : 数学期望,离散时的公式是E(X) = X1*p(X1) + X2*p(X2) + …… + Xn*p(Xn) p(xi)的是 ...
- 【CF 453A】 A. Little Pony and Expected Maximum(期望、快速幂)
A. Little Pony and Expected Maximum time limit per test 1 second memory limit per test 256 megabytes ...
- Codeforces Round #259 (Div. 1) A. Little Pony and Expected Maximum 数学公式结论找规律水题
A. Little Pony and Expected Maximum Time Limit: 1 Sec Memory Limit: 256 MB 题目连接 http://codeforces.c ...
- E. Little Pony and Expected Maximum(组合期望)
题目描述: Little Pony and Expected Maximum time limit per test 1 second memory limit per test 256 megaby ...
- 嘴巴题9 Codeforces 453A. Little Pony and Expected Maximum
A. Little Pony and Expected Maximum time limit per test 1 second memory limit per test 256 megabytes ...
- CF453A Little Pony and Expected Maximum 期望dp
LINK:Little Pony and Expected Maximum 容易设出状态f[i][j]表示前i次最大值为j的概率. 转移很显然 不过复杂度很高. 考虑优化.考虑直接求出最大值为j的概率 ...
- CodeForces - 453A Little Pony and Expected Maximum
http://codeforces.com/problemset/problem/453/A 题目大意: 给定一个m面的筛子,求掷n次后,得到的最大的点数的期望 题解 设f[i]表示掷出 <= ...
- codeforces——Little Pony and Expected Maximum
/* 我们枚举每次选择最大数值的情况:m个数, 投掷n次 最大值是1: 1种 2: 2^n-1 3: 3^n-2^n ..... m: m^n-(m-1)^n 所以最后的结果=sum((k/m)^n ...
随机推荐
- 【Flutter】容器类组件之填充
前言 Padding可以给其子节点添加填充(留白). 接口描述 class EdgeInsets extends EdgeInsetsGeometry { // 分别指定四个方向的填充 const E ...
- Nginx基础知识学习(安装/进程模型/事件处理机制/详细配置/定时切割日志)
一.Linux下Nginx的安装 1.去官网 http://nginx.org/download/下载对应的Nginx安装包,推荐使用稳定版本. 2.上传Nginx到Linux服务器. 3.安装依赖环 ...
- mysql中的基本注入函数
1. 常见数据库注入函数: MYSQL: and length((user))>10 ACCESS: and (select count() from MSysAccessObject)> ...
- Kaggle泰坦尼克-Python(建模完整流程,小白学习用)
参考Kernels里面评论较高的一篇文章,整理作者解决整个问题的过程,梳理该篇是用以了解到整个完整的建模过程,如何思考问题,处理问题,过程中又为何下那样或者这样的结论等! 最后得分并不是特别高,只是到 ...
- LeetCode404.左叶子之和
题目 法一.广度优先搜索 1 class Solution { 2 public: 3 int sumOfLeftLeaves(TreeNode* root) { 4 if(root == NULL) ...
- ctfshow—web—web签到题
打开靶机,发现只有一句话 查看源码 发现一段字符串,猜是base64加密 拿到flag
- Jquery实现对Array数组实现类似Linq的Lambda表达式的Where方法筛选
平时使用Linq,习惯了Lambda表达式,用着非常顺手,奈何在Jquery里面不能这样用,只能循环一个个判断.趁空闲时间找了找,自己写了这样的扩展方法.目前写出了三种方案,没有比较性能,觉得都可以用 ...
- [Usaco2009 Feb]Bullcow 牡牛和牝牛
原题链接https://www.lydsy.com/JudgeOnline/problem.php?id=3398 容易想到的一种\(dp\)就是:设\(dp[i][j]\)表示前\(i\)头牛里面有 ...
- Trove自动钓鱼脚本(国际服
#WinActivateForce ; Script config. Do NOT change value here, might working inproperly! global Versio ...
- Linux 下安装 JDK
JDK 依赖包: yum install glibc.i686 卸载原有的 JDK 查看本机已安装软件:rpm -qa 查看与java相关的软件:rpm -qa | grep java 删除自带软件: ...