PROBLEM STATEMENT
Given the width and height of a rectangular grid, return the total number of rectangles (NOT
counting squares) that can be found on this grid.
For example, width = 3, height = 3 (see diagram below):
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In this grid, there are 4 2x3 rectangles, 6 1x3 rectangles and 12 1x2 rectangles. Thus there is a
total of 4 + 6 + 12 = 22 rectangles. Note we don't count 1x1, 2x2 and 3x3 rectangles because they
are squares.
DEFINITION
Class:RectangularGrid
Method:countRectangles
Parameters:int, int
Returns:long long
Method signature:long long countRectangles(int width, int height)
NOTES
-rectangles with equals sides (squares) should not be counted.
CONSTRAINTS
-width and height will be between 1 and 1000 inclusive.
EXAMPLES
0)
3
3
Returns: 22
See above
1)
5
2
Returns: 31
__ __ __ __ __
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In this grid, there is one 2x5 rectangle, 2 2x4 rectangles, 2 1x5 rectangles, 3 2x3 rectangles, 4
1x4 rectangles, 6 1x3 rectangles and 13 1x2 rectangles. Thus there is a total of 1 + 2 + 2 + 3 + 4
+ 6 + 13 = 31 rectangles.
2)
10
10
Returns: 2640
3)
1
1
Returns: 0
4)
592
964
Returns: 81508708664
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