lightoj1064_简单dp

http://lightoj.com/volume_showproblem.php?problem=1064

n common cubic dice are thrown. What is the probability that the sum of all thrown dice is at least x?

Input

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each test case contains two integers n (1 ≤ n < 25) and x (0 ≤ x < 150). The meanings of n and x are given in the problem statement.

Output

For each case, output the case number and the probability in 'p/q' form where p and q are relatively prime. If q equals 1 then print p only.

Sample Input	Output for Sample Input
7 3 9 1 7 24 24 15 76 24 143 23 81 7 38	Case 1: 20/27 Case 2: 0 Case 3: 1 Case 4: 11703055/78364164096 Case 5: 25/4738381338321616896 Case 6: 1/2 Case 7: 55/46656

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <vector>
#include <ctime>
#include <queue>
#include <list>
#include <set>
#include <map>
using namespace std;
#define INF 0x3f3f3f3f
typedef long long LL;

LL dp[30][150];
int main()
{
    int t, n, x;
    scanf("%d", &t);
    for(int ca = 1; ca <= t; ca++)
    {
        scanf("%d %d", &n, &x);
        memset(dp, 0, sizeof(dp));
        for(int i = 1; i <= 6; i++)
            dp[1][i] = 1;
        LL sum = 6;
        for(int i = 2; i <= n; i++)
        {
            sum *= 6;
            for(int j = i*6; j > 0; j--)
            {
                for(int k = 1; k <= 6; k++)
                {
                    if(j-k > 0)
                        dp[i][j] += dp[i-1][j-k];
                }            
            }
        }
        LL res = 0;
        for(int i = x; i <= n * 6; i++)
            res += dp[n][i];
        printf("Case %d: ", ca);
        if(res == 0){
            printf("0
");
            continue;
        }
        if(sum == res)
        {
            printf("1
");
            continue;
        }
        LL te = __gcd(res, sum);
        printf("%lld/%lld
", res/te, sum/te);
    }
    return 0;
}