BeautifulHexagonalTilings | Topcoder Archive

Problem Statement

Consider a hexagonal grid with 6 sides, with the side lengths given by the int[] s (in the clockwise order), as shown in the following picture:

Count the number of ways to color each cell with one of two colors, black or white, such that every non-border black cell has exactly a black neighbors, and every non-border white cell has exactly b white neighbors (a cell is called non-border if and only if it has exactly 6 neighbors in the grid).

Definition

Class:: BeautifulHexagonalTilings
Method:: howMany
Parameters:: int[], int, int
Returns:: int
Method signature:: int howMany(int[] s, int a, int b)
(be sure your method is public)

Constraints

s will contain exactly 6 elements.
Each element of s will be between 2 and 6, inclusive.
a and b will each be between 0 and 6, inclusive.
s will define a valid hexagonal grid.
The answer will always fit into an int.

Examples

```
{2,2,2,2,2,2}
```
```
6
```
```
6
```
```
Returns: 2
```
Either all white or all black.
```
{6,6,6,6,6,6}
```
```
6
```
```
6
```
```
Returns: 2
```
The field is bigger, but still all white or all black.
```
{2,2,2,2,2,2}
```
```
2
```
```
2
```
```
Returns: 30
```
```
{4,4,3,5,3,4}
```
```
4
```
```
1
```
```
Returns: 213
```
The grid from the picture.

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