zoj 3822 Domination(2014牡丹江区域赛D题) （概率dp）

3799567	2014-10-14 10:13:59	Accepted	3822	C++	1870	71760	njczy2010
3799566	2014-10-14 10:13:25	Memory Limit Exceeded	3822	C++	0	131073	njczy2010

sign，，，太弱了，，，

DominationTime Limit: 8 Seconds Memory Limit: 131072 KB Special Judge
Edward is the headmaster of Marjar University. He is enthusiastic about chess and often plays chess with his friends. What's more, he bought a large decorative chessboard with N rows and M columns.

Every day after work, Edward will place a chess piece on a random empty cell. A few days later, he found the chessboard was dominated by the chess pieces. That means there is at least one chess piece in every row. Also, there is at least one chess piece in every column.

"That's interesting!" Edward said. He wants to know the expectation number of days to make an empty chessboard of N × M dominated. Please write a program to help him.

Input

There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

There are only two integers N and M (1 <= N, M <= 50).

Output

For each test case, output the expectation number of days.

Any solution with a relative or absolute error of at most 10-8 will be accepted.

Sample Input

2
1 3
2 2

Sample Output

3.000000000000
2.666666666667

Author: JIANG, Kai

#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<queue>
#include<map>
#include<set>
#include<string>
//#include<pair>

#define N 55
#define M 1000005
#define mod 1073741824
//#define p 10000007
#define mod2 100000000
#define ll long long
#define LL long long
#define maxi(a,b) (a)>(b)? (a) : (b)
#define mini(a,b) (a)<(b)? (a) : (b)

using namespace std;

int T;
int n,m;
double dp

[N*N];
double ans;
int tot;

void ini()
{
ans=0;
memset(dp,0,sizeof(dp));
scanf("%d%d",&n,&m);
tot=n*m;
}

void solve()
{
int i,j,k;
dp[1][1][1]=1;
for(i=1;i<=n;i++){
for(j=1;j<=m;j++){
if(i==1 && j==1) continue;
for(k=max(i,j);k<=i*j;k++){
//printf("  i=%d j=%d k=%d dp=%.5f add=%.5f\n",i,j,k,dp[i][j-1][k-1],dp[i][j-1][k-1]*(m-j)*i/(tot-(k-1)));
if(i==n && j==m){
dp[i][j][k]=dp[i-1][j][k-1]*(n-i+1)*j/(tot-(k-1))
+dp[i][j-1][k-1]*(m-j+1)*i/(tot-(k-1))
+dp[i-1][j-1][k-1]*(n-i+1)*(m-j+1)/(tot-(k-1));
}
else
dp[i][j][k]=dp[i-1][j][k-1]*(n-i+1)*j/(tot-(k-1))
+dp[i][j-1][k-1]*(m-j+1)*i/(tot-(k-1))
+dp[i-1][j-1][k-1]*(n-i+1)*(m-j+1)/(tot-(k-1))
+dp[i][j][k-1]*(i*j-(k-1))/(tot-(k-1));
// printf("  aft i=%d j=%d k=%d dp=%.5f\n",i,j,k,dp[i][j][k]);
}
}
}
//for(i=1;i<=n;i++){
//    for(j=1;j<=m;j++){
//        for(k=max(i,j);k<=i*j;k++){
//           printf(" i=%d j=%d k=%d dp=%.5f\n",i,j,k,dp[i][j][k]);
//        }
//    }
// }

for(k=0;k<=tot;k++){
ans+=dp
[m][k]*k;
}
}

void out()
{
printf("%.10f\n",ans);
}

int main()
{
// freopen("data.in","r",stdin);
//freopen("data.out","w",stdout);
scanf("%d",&T);
// for(int ccnt=1;ccnt<=T;ccnt++)
while(T--)
// while(scanf("%s",s1)!=EOF)
{
//if(n==0 && k==0 ) break;
//printf("Case %d: ",ccnt);
ini();
solve();
out();
}

return 0;
}