RectangularGrid | Topcoder Archive

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):

 __ __ __
|__|__|__|
|__|__|__|
|__|__|__|

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
Method signature:: long countRectangles(int width, int height)
(be sure your method is public)

Notes

rectangles with equals sides (squares) should not be counted.

Constraints

width and height will be between 1 and 1000 inclusive.

Examples

```
3
```
```
3
```
```
Returns: 22
```
See above
```
5
```
```
2
```
```
Returns: 31
```
__ __ __ __ __ |__|__|__|__|__| |__|__|__|__|__| 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.
```
10
```
```
10
```
```
Returns: 2640
```
```
1
```
```
1
```
```
Returns: 0
```
```
592
```
```
964
```
```
Returns: 81508708664
```

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