Topcoder SRM579 1000pts

#include<map>
#include<stack>
#include<queue>
#include<cstdio>
#include<string>
#include<vector>
#include<cstring>
#include<complex>
#include<iostream>
#include<assert.h>
#include<algorithm>
using namespace std;
#define inf 1001001001
#define infll 1001001001001001001LL
#define ll long long
#define dbg(vari) cerr<<#vari<<" = "<<(vari)<<endl
#define gmax(a,b) (a)=max((a),(b))
#define gmin(a,b) (a)=min((a),(b))
#define Ri register int
#define gc getchar()
#define il inline
il int read(){
    bool f=true;Ri x=0;char ch;while(!isdigit(ch=gc))if(ch==‘-‘)f=false;while(isdigit(ch)){x=(x<<1)+(x<<3)+ch-‘0‘;ch=gc;}return f?x:-x;
}
#define gi read()
#define ig read()
#define FO(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout);
int n;double ans,R[55],P[55],S[55];
double dp[55][55][55][55];
int main(){
    FO(rps);
    n=gi;
    for(int i=0;i<n;i++){
        R[i]=gi;R[i]/=300;
        P[i]=gi;P[i]/=300;
        S[i]=gi;S[i]/=300;
    }
    for(int a=0;a<n;a++){
        dp[a][0][0][0]=1.0;
        for(int i=0;i<n;i++)
            for(int j=i;j+1;j--)
                for(int k=i-j;k+1;k--)
                    for(int s=i-j-k;s+1;s--) {
                        if(i!=a){
                        dp[a][j+1][k][s]=dp[a][j+1][k][s]+1.0*(j+k+s+1)/(i+1)*R[i]*dp[a][j][k][s];
                        dp[a][j][k+1][s]=dp[a][j][k+1][s]+1.0*(j+k+s+1)/(i+1)*P[i]*dp[a][j][k][s];
                        dp[a][j][k][s+1]=dp[a][j][k][s+1]+1.0*(j+k+s+1)/(i+1)*S[i]*dp[a][j][k][s];        
                        }dp[a][j][k][s]=dp[a][j][k][s]*(1-1.0*(j+k+s)/(i+1));        
                    }    
    }
    for(int i=0;i<n;i++){
        for(int j=0;j<n-i;j++){
            for(int k=0;k<n-i-j;k++){
                double r,p,s;
                r=p=s=0;
                //face i rock k scissor j paper
                for(int a=0;a<n;a++){
                    double t=dp[a][i][j][k],m=n-i-j-k;
                    r=r+dp[a][i][j][k]/m*R[a];
                    p=p+dp[a][i][j][k]/m*P[a];
                    s=s+dp[a][i][j][k]/m*S[a];
                }
                double tmp=0.0;
                gmax(tmp,3*r+p);
                gmax(tmp,3*p+s);
                gmax(tmp,3*s+r);
                /*
                old version fucking possiblities
                gmax(ans,3*r+p);
                gmax(ans,3*p+s);
                gmax(ans,3*s+r);*/
                ans+=tmp;        
            }
        }
    }
    printf("%.9lf",ans);
    return 0;
}