RectangleDivision | Topcoder Archive

Problem Statement

Consider an a by b rectangle, composed of a*b unit squares. Your task is to count the number of ways in which this rectangle can be divided into two contiguous sections, each consisting of 1 or more unit squares. Each section must contain at least 1 square on the edge of the rectangle. A section is contiguous if each square in the section is connected to each other square in the section via a path of horizontally or vertically adjacent squares that are all within the section.

Definition

Class:: RectangleDivision
Method:: count
Parameters:: int, int
Returns:: int
Method signature:: int count(int a, int b)
(be sure your method is public)

Constraints

a will be between 1 and 6, inclusive.
b will be between 2 and 6, inclusive.

Examples

```
1
```
```
3
```
```
Returns: 2
```
There are two different ways to split up this rectangle, where '#' represents one section, and '.' the other: ##. #..
```
3
```
```
2
```
```
Returns: 15
```
Here are the 15 ways: #. .# .. .. #. .# .. .. .. .. .. .. #. .# #. .# .. .. #. .# .. .. #. .# ## .. ## ## ## ## #. .. .. #. .# #. .# #. .. ## ## ## .. .. #.
```
3
```
```
3
```
```
Returns: 52
```

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