Hdu5245 --- Joyful (expected), joyful

Hdu5245 --- Joyful (expected), joyful

Problem Description
Sakura has a very magical tool to paint Wils. 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
We have carefully selected several similar problems for you: 5244 5243 5242 5241 5240

Consider the probability of each grid being coated, and add the probability to the end.

/*************************************** * *********************************> File Name: hdu5245.cpp> Author: ALex> Mail: zchao1995@gmail.com> Created Time: thursday, May 28, 2015 ******************************** **************************************** /# include <functional> # include <algorithm> # include <iostream> # include <fstream> # include <cstring> # include <cstdio> # include <cmath> # include <cstdlib> # include <queue> # include <stack> # include <map> # include <bitset> # include <set> # include <vector> using namespace std; const double pi = acos (-1.0); const int inf = 0x3f3f3f3f; const double eps = 1e-15; typedef long LL; typedef pair <int, int> PLL; int main () {int t, icase = 1; scanf ("% d", & t); while (t --) {int n, m, k; scanf ("% d", & n, & m, & k); double ans = 0; for (int I = 1; I <= n; ++ I) {for (int j = 1; j <= m; ++ j) {LL ways = (LL) (I-1) * (I-1) * m; ways + = (LL) (j-1) * (j-1) * n; ways + = (LL) (n-I) * (n-I) * m; ways + = (LL) (m-j) * n; ways-= (LL) (I-1) * (I-1) * (j-1) * (j-1); ways-= (LL) (I-1) * (I-1) * (m-j); ways-= (LL) (j-1) * (j-1) * (n-I); ways-= (LL) (n-I) * (m-j) * (m-j); LL sum = (LL) m * n; double p = ways * 1.0/sum; double tmp = 1; for (int l = 1; l <= k; ++ l) {tmp * = p;} ans + = (1-tmp );}} printf ("Case # % d: %. 0f \ n ", icase ++, ans);} return 0 ;}