TopCoder Statistics - Problem Statement

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: #. .# .. .. #. .# .. .. .. .. .. .. #. .# #. .# .. .. #. .# .. .. #. .# ## .. ## ## ## ## #. .. .. #. .# #. .# #. .. ## ## ## .. .. #.
1

2

Returns: 1
1

3

Returns: 2
1

4

Returns: 3
1

5

Returns: 4
1

6

Returns: 5
2

2

Returns: 6
2

3

Returns: 15
2

4

Returns: 28
2

5

Returns: 45
2

6

Returns: 66
3

2

Returns: 15
3

3

Returns: 52
3

4

Returns: 143
3

5

Returns: 350
3

6

Returns: 799
4

2

Returns: 28
4

3

Returns: 143
4

4

Returns: 614
4

5

Returns: 2431
4

6

Returns: 9184
5

2

Returns: 45
5

3

Returns: 350
5

4

Returns: 2431
5

5

Returns: 16000
5

6

Returns: 102147
6

2

Returns: 66
6

3

Returns: 799
6

4

Returns: 9184
6

5

Returns: 102147
6

6

Returns: 1114394

Statistics

Problem Statement for "RectangleDivision"

Problem Statement

Definition

Constraints

Examples