How many subrectangle exists on a m x n grid
algorithm
Solution
The answer is `m(m+1)n(n+1)/4`.
a rectangle is defined by its two projections on the x-axis and on the y-axis.
projection on x-axis : number of pairs (a,b) such that 1 <= a <= b <= m = m(m+1)/2
idem for y-axis
Problem
Given a `m x n` grid, how many unique sub-rectangles exist on such a grid? For example, `1 x 1` grid has 1 sub-rectangle. `1 x 2` grid has 3 sub-rectangles. I am looking for a general formula that can be used to directly compute the number existing sub-rectangle.