ZOJ 2949 Coins of Luck（概率dp求期望）

标签：数学   zoj   dp   期望   

题目链接：http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=1948

Luck is the key to life. When I have to decide something, I will make my decision by flipping a coin. And then, I have two things to do. First, I have the decision made. Second, I go to the nearest church and donate the coin.

But there are always too many things I have to decide. For example, what should I eat today for lunch? OK, now we are talking about a decision, so let us assume that I have two kinds of food: quick-served noodle A and quick-served noodle B.

I just have bought N bowls of noodle A and N bowls of noodle B. If I have some space to make a decision (i.e. having two kinds of quick-served noodle to choose from), then I will flip a coin to decide which kind of noodle to eat.

My question is, before I eat up all 2 * N bowls of quick-served noodle, what is the mathematical expectation of the number of coins I will have to donate.

Input

Standard input will contain multiple test cases. The first line of the input is a single integer T (1 <= T <= 1000) which is the number of test cases. And it will be followed by T consecutive test cases.

Each test case contains an integer N (1 <= N <= 1000).

Output

Sample Input

2
1
2

Sample Output

1.00
2.50

题意：

有一个人要吃A和B两种面，分别n碗；每一次用抛硬币的方式决定吃哪一种面！

求吃完面需要跑硬币的次数的期望！

PS:

dp[i][j]:表示吃了A种面 i 碗，B种面j碗的期望！

dp[i][j] = dp[i-1][j] * 0.5 + dp[i][j-1]*0.5 + 1; 因为从dp[i][j] 变为dp[i-1][j] 或者dp[i][j-1]还需要跑一次硬币！

代码如下：

#include <cstdio>
#include <cstring>
double dp[1017][1017];
void init()
{
    dp[0][0] = 0;
    for(int i = 0; i <= 1000; i++)
    {
        dp[i][0] = 0;
        dp[0][i] = 0;
    }
    for(int i = 1; i <= 1000; i++)
    {
        for(int j = 1; j <= 1000; j++)
        {
            dp[i][j] = dp[i-1][j]*0.5 + dp[i][j-1]*0.5+1;
        }
    }
}
int main()
{
    int t;
    init();
    scanf("%d",&t);
    while(t--)
    {
        int n;
        scanf("%d",&n);
        printf("%.2lf\n",dp[n][n]);
    }
    return 0;
}

ZOJ 2949 Coins of Luck（概率dp求期望）

标签：数学   zoj   dp   期望   

原文地址：http://blog.csdn.net/u012860063/article/details/44904259