Joyful

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1243    Accepted Submission(s): 546

Problem Description

Sakura has a very magical tool to paint walls. One day, kAc asked Sakura to paint a wall that looks like an M×N matrix. The wall has M×N squares in all. In the whole problem we denotes (x,y) to be the square at the x-th row, y-th column. Once Sakura has determined two squares (x1,y1) and (x2,y2), she can use the magical tool to paint all the squares in the sub-matrix which has the given two squares as corners.

However, Sakura is a very naughty girl, so she just randomly uses the tool for K times. More specifically, each time for Sakura to use that tool, she just randomly picks two squares from all the M×N squares, with equal probability. Now, kAc wants to know the expected number of squares that will be painted eventually.

Input

The first line contains an integer T(T≤100), denoting the number of test cases.

For each test case, there is only one line, with three integers M,N and K.
It is guaranteed that 1≤M,N≤500, 1≤K≤20.

Output

For each test case, output ‘‘Case #t:‘‘ to represent the t-th case, and then output the expected number of squares that will be painted. Round to integers.

Sample Input

2
3 3 1
4 4 2

Sample Output

Case #1: 4
Case #2: 8

Hint

The precise answer in the first test case is about 3.56790123.

Source

The 2015 ACM-ICPC China Shanghai Metropolitan Programming Contest

Recommend

代码较挫，

 1 #include <iostream>
 2 #include <stdio.h>
 3 using namespace std;
 4
 5 using namespace std;
 6
 7 #define LL long long
 8
 9 long long C(LL  a,LL b)
10 {
11     return a * b * a * b;
12 }
13 int main()
14 {
15     long long T,m,n,k;
16     int cas = 0;
17     scanf("%lld",&T);
18     while(T--)
19     {
20         LL sum;
21         double ans=0, p;
22         scanf("%lld%lld%lld",&m,&n,&k);
23         for(LL i=0; i<m; i++)
24         {
25             for(LL j=0; j<n; j++)
26             {
27                sum = C(i,n)+C((m-i-1),n)+C(j,m)+C((n-j-1),m);
28                sum = sum - C(i,j) - C(i,(n-j-1)) - C((m-i-1),j ) - C((m-i-1),(n-j-1)) ;
29                p = sum * 1.0 / C(m,n);
30
31 double tmp=1;
32                for (LL jj = 1; jj <= k; ++jj)
33                     tmp *= p;
34                ans=ans+1-tmp;
35             }
36         }
37         printf("Case #%d: %.0f\n",++cas,ans);
38     }
39     return 0;
40 }