Given a grid of size m x n, calculate the total number of rectangles contained in this rectangle. All integer sizes and positions are counted.
Examples:
numberOfRectangles(3, 2) == 18
numberOfRectangles(4, 4) == 100
Here is how the 3x2 grid works:
1 rectangle of size 3x2:
[][][]
[][][]
2 rectangles of size 3x1:
[][][]
4 rectangles of size 2x1:
[][]
2 rectangles of size 2x2
[][]
[][]
3 rectangles of size 1x2:
[]
[]
6 rectangles of size 1x1:
[]
As you can see (1 + 2 + 4 + 2 + 3 + 6) = 18, and is the solution for the 3x2 grid.
There is a very simple solution to this!