Throwing Dice (probabilistic DP)

c-throwing Dice

Time limit:2000MS Memory Limit:32768KB 64bit IO Format:%lld &%llu

Lightoj 1064 Udebug

Description

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

Input

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

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

Output

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

Sample Input

7

3 9

1 7

24 24

15 76

24 143

23 81

7 38

Sample Output

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

The game did not read the title, this is a simple probability DP, the first line is the case number T, and then N, M is the probability that N dice throw at least m.

DP[I][J] Represents the I dice, throw the J-type number

Dp[i+1][j+k]=sigma (Dp[i][j]) (1<=k<=6)

1#include <cstdio>2#include <iostream>3#include <cstring>4 using namespacestd;5 6__int64 dp[ -][155];7 8 __int64 gcd (__int64 x,__int64 y)9 {Ten     returnY?GCD (y,x%y): x; One } A  - intMain () - { the __int64 up,down,g; -     intt,n,x,i,j,k; -  -      for(i=1; i<=6; i++)//a dice +dp[1][i]=1; -      for(i=1;i< -; i++)//Dice +     { A          for(j=i;j<=6*i;j++)//all the points in this dice at         { -              for(k=1; k<=6; k++)//the point of the next dice -dp[i+1][j+k]+=Dp[i][j]; -         } -     } -  inscanf"%d",&T); -      for(intcas=1; cas<=t;cas++) to     { +scanf"%d%d",&n,&x); -         if(x>n*6) the         { *printf"Case %d:0\n", CAs); $             Continue;Panax Notoginseng         } -         if(x<=N) the         { +printf"Case %d:1\n", CAs); A             Continue; the         } +up=0, down=1; -          for(i=x;i<=n*6; i++) $up+=Dp[n][i]; $          for(j=0; j<n;j++) down*=6;//all the dice could be the case -g=gcd (up,down); -printf"Case %d:%i64d/%i64d\n", cas,up/g,down/g); the     } -     return 0;Wuyi}

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Throwing Dice (probabilistic DP)