Codeforces Round #185 (Div. 2) B. Archer 水题

B. Archer

Time Limit: 20 Sec

Memory Limit: 256 MB

题目连接

http://codeforces.com/contest/312/problem/B

Description

SmallR is an archer. SmallR is taking a match of archer with Zanoes. They try to shoot in the target in turns, and SmallR shoots first. The probability of shooting the target each time is  for SmallR while  for Zanoes. The one who shoots in the target first should be the winner.

Output the probability that SmallR will win the match.

Input

A single line contains four integers .

Output

Print a single real number, the probability that SmallR will win the match.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Sample Input

1 2 1 2

Sample Output

0.666666666667

HINT

 

题意

第一个人有a/b的概率射中靶子，第二个人有c/d的概率射中靶子，两个人轮流射

然后问你有多大的概率第二个人最先射中靶子

题解：

水题啦，很容易推公式，发现是一个等比数列，然后求和就好了

也可以不求和，直接暴力for也行

代码：

#include<iostream>
#include<stdio.h>
#include<math.h>
using namespace std;


int main()
{
    double a,b,c,d;
    cin>>a>>b>>c>>d;
    double p1 = a/b,p2 = c/d;
    double ans = 0;
    double p = 1;
    for(int i=0;i<10000;i++)
    {
        ans += p*(1-p1)*p2;
        p = p * (1-p1) * (1-p2);
    }
    printf("%.10f\n",1-ans);
}