CF540D Bad Luck Island

// Problem: CF540D Bad Luck Island
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/CF540D
// Memory Limit: 250 MB
// Time Limit: 2000 ms
// Author:Cutele
// 
// Powered by CP Editor (https://cpeditor.org)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll>PLL;
typedef pair<int, int>PII;
typedef pair<double, double>PDD;
#define I_int ll
inline ll read()
{
    ll x = 0, f = 1;
    char ch = getchar();
    while(ch < '0' || ch > '9')
    {
        if(ch == '-')f = -1;
        ch = getchar();
    }
    while(ch >= '0' && ch <= '9')
    {
        x = x * 10 + ch - '0';
        ch = getchar();
    }
    return x * f;
}
  
inline void out(ll x){
    if (x < 0) x = ~x + 1, putchar('-');
    if (x > 9) out(x / 10);
    putchar(x % 10 + '0');
}
  
inline void write(ll x){
    if (x < 0) x = ~x + 1, putchar('-');
    if (x > 9) write(x / 10);
    putchar(x % 10 + '0');
}
  
#define read read()
#define closeSync ios::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define multiCase int T;cin>>T;for(int t=1;t<=T;t++)
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define repp(i,a,b) for(int i=(a);i<(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define perr(i,a,b) for(int i=(a);i>(b);i--)
ll ksm(ll a, ll b,ll p)
{
    ll res = 1;
    while(b)
    {
        if(b & 1)res = res * a%p;
        a = a * a %p;
        b >>= 1;
    }
    return res;
}

double dp[110][110][110];
int r,s,p;

int main(){
	r=read,s=read,p=read;
	dp[r][s][p]=1.0;
	for(int i=r;i>=0;i--)
		for(int j=s;j>=0;j--)
			for(int k=p;k>=0;k--){
				int sum=i*j+i*k+j*k;
				if(i&&j) dp[i][j-1][k]+=dp[i][j][k]*i*j*1.0/sum;
				if(i&&k) dp[i-1][j][k]+=dp[i][j][k]*i*k*1.0/sum;
				if(j&&k) dp[i][j][k-1]+=dp[i][j][k]*j*k*1.0/sum;
			}
	double sumr=0,sums=0,sump=0;
	rep(i,0,r) sumr+=dp[i][0][0];
	rep(i,0,s) sums+=dp[0][i][0];
	rep(i,0,p) sump+=dp[0][0][i];
	printf("%.9f %.9f %.9f
",sumr,sums,sump);
	return 0;
}