MountainMap | Topcoder Archive

Problem Statement

A mountain map is a NxM rectangular grid where each cell has a height. The heights are positive integers between 1 and N*M, inclusive, and no two distinct cells have equal heights. Two cells are called neighboring if they share a side or a corner. A cell is called locally minimal if its height is less than the heights of all its neighboring cells.

You are given a String[] data. The j-th character of the i-th element of data is 'X' if the j-th cell in the i-th row of the mountain map is locally minimal, and '.' otherwise. Calculate the number of distinct mountain maps that match the data. Return the result modulo 12345678.

Definition

Class:: MountainMap
Method:: count
Parameters:: String[]
Returns:: int
Method signature:: int count(String[] data)
(be sure your method is public)

Constraints

data will contain between 1 and 4 elements, inclusive.
Each element of data will contain between 1 and 7 characters, inclusive.
All elements of data will contain the same number of characters.
Each character in each element of data will be '.' or uppercase 'X'.

Examples

```
{".X."}
```
```
Returns: 2
```
The middle cell is lower than its neighbors, so its height is 1. There are two variants of heights for the other cells: the left cell's height is 2 and the right cell's height is 3, or vice versa.
```
{"X.",
 ".X"}
```
```
Returns: 0
```
No two neighboring cells can both be locally minimal, so the answer is 0.
```
{"...",
 "..."}
```
```
Returns: 0
```
Each mountain map contains at least one locally minimal cell.
```
{"X.",
 "..",
 ".X"}
```
```
Returns: 60
```
```
{"X.X",
 "...",
 "X.X"}
```
```
Returns: 4800
```
```
{"..X.."}
```
```
Returns: 6
```

{"....X.",
 "......",
 ".X...X"}

Returns: 869490

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