Light OJ 1050 / Expected Value

/***
 created: 2022-08-29-01.49.51
***/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename U> using ordered_set=tree<U, null_type,less<U>,rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long
#define test int tt; cin>>tt; for(int cs=1;cs<=tt;cs++)
#define get_lost_idiot return 0
#define nl '\n'

double dp[2][501][501];
bool v[2][501][501];

double solve(ll r,ll b,ll c)
{
    if(r==0 && b==1) return 1.00;
    if(v[c][r][b]) return dp[c][r][b];

    double ans=0.00;

    v[c][r][b]=1;

    if(!c)
    {
        if(r)
        {
            ans+=((1.00*r)/((r+b)*1.00))*solve(r-1,b,c^1);
        }
        if(b)
        {
            ans+=((1.00*b)/((r+b)*1.00))*solve(r,b-1,c^1);
        }
    }
    else
    {
        if(b)
        {
            ans+= /*((1.00*b)/((r+b)*1.00))* */ solve(r,b-1,c^1);
            // this can't contribute to my winning probability
        }
    }

    return dp[c][r][b]=ans;
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    test
    {
        ll r,b;

        cin>>r>>b;

        //memset(v,0,sizeof v);

        cout<<"Case "<<cs<<": "<<fixed<<setprecision(12)<<solve(r,b,0)<<nl;
    }

    get_lost_idiot;
}