XDOJ1270 - Rectangle Counting

Description

The length and the width of the following figure are 2. How many rectangles are there in this figure?



There are 9 rectangles in this figure. They are 4 rectangles with each side 1*1, 2 rectangles with each side 1*2, 2 rectangles with each side 2*1 and 1 rectangle with each side 2*2.

Input
The input consists of several test cases.

　　　The first line of the input contains a single integer T (0 < T ≤ 20), the number of test cases.

Then Followed by T lines, each line gives a test case which contains two positive integers N and M, which means the length and the width of the figure( 1≤ N, M ≤ 10 ).
Output
　　For each test case, output an integer indicating the number of rectangles in the figure.
Sample Input
2

1 1

2 2

Sample Output
1

9

解题 思路:

因为矩形的长和宽的选择没有相互关系，那么我们可以分别统计矩形的长和宽有多少种选择，然后由乘法原理得出矩形个数。以长的选择为例：网格长为N，则共有N+1个格点，于是长的选择方式为： C（N+1，2）=N*（N+1）/2 同理，宽的选择方式为： C（M+1，2）=M*（M+1）/2 矩形个数为N*（N+1）*M*（M+1）/4

#include<iostream>

using namespace std;

int main()
{
int caseN;
cin>>caseN;
while(caseN--)
{
int N,M;
cin>>N>>M;
cout<<N*(N+1)*M*(M+1)/4<<endl;
}
return 0;
}