hdu 5194 DZY Loves Balls

Problem Description

There are n black balls and m white balls in the big box.
Now, DZY starts to randomly pick out the balls one by one. It forms a sequence S. If at the i-th operation, DZY takes out the black ball, Si=1, otherwise Si=0.
DZY wants to know the expected times that '01' occurs in S.

 

Input

The input consists several test cases. (TestCase≤150)
The first line contains two integers, n, m(1≤n,m≤12)

 

Output

For each case, output the corresponding result, the format is p/q(p and q are coprime)

 

Sample Input

1 1 2 3

 

Sample Output

1/2 6/5

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int m,n;
void build(int x,int y,int t1,int t2,int &ans1,int &ans2)
{
    int a,b;
    if (t2==m) {ans1=1;ans2=1;return ;}
    if (t1==n)
    {
        if (x==0) ans2=1;
        else ans2=0;
        ans1=1;
        return ;
    }
    build(y,0,t1,t2+1,ans1,ans2);
    a=ans1;
    b=ans2;
    build(y,1,t1+1,t2,ans1,ans2);
    a+=ans1;
    b+=ans2;
    if (x==0&&y==1) b+=a;
    ans1=a;
    ans2=b;
}
int main()
{
    int a,b,c,ans1,ans2;
    while (~scanf("%d%d",&n,&m))
    {
        build(-1,0,0,1,ans1,ans2);
        a=ans1;b=ans2;
        build(-1,1,1,0,ans1,ans2);
        a+=ans1;b+=ans2;
        n=b;
        m=a;
        a=max(n,m);
        b=min(n,m);
        c=1;
        while (c)
        {
            c=a%b;
            a=b;
            b=c;
        }
        printf("%d/%d
",n/a,m/a);
    }
    return 0;
}