ColoringCount | Topcoder Archive

Problem Statement

You want to know how many distinct regions there are on a particular page in a color-by-number book. You will be given a String[] input representing the page we are examining. Each element of input will represent a horizontal section of the page. Each character in input will represent a space on the page. If a particular character in input is a (quotes for clarity) '.', then the space it represents is blank. If a particular character in input is a (quotes for clarity) '#', then the space it represents is part of a line. 2 spaces in input are in the same region if there is a path from one to the other consisting of only horizontal or vertical moves that never crosses a line. This path may not leave the page. In addition, spaces that belong to lines are never considered part of regions. For example:

input = {"...#...",
         "...#...",
         "#######",
         "...#...",
         "###...#"}

The page above has 4 regions. These regions are labeled below:

Given a String[] input representing a page in the coloring book, return how many distinct regions there are. In the above example, your method would return 4.

Definition

Class:: ColoringCount
Method:: howMany
Parameters:: String[]
Returns:: int
Method signature:: int howMany(String[] input)
(be sure your method is public)

Constraints

input will contain between 1 and 20 elements inclusive
Each element of input will contain between 1 and 20 characters inclusive
Each element of input will contain the same number of characters
Each element of input will only contain (quotes for clarity) periods '.', or number-signs '#'

Examples

{"...#...",
 "...#...",
 "#######",
 "...#...",
 "###...#"}

Returns: 4

Example from above.

```
{"#"}
```
```
Returns: 0
```
A single line can't be a region.
```
{"."}
```
```
Returns: 1
```
A single space is the only region.

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

Returns: 1

One big space.

{".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#",
 "#.#.#.#.#.#.#.#.#.#.",
 ".#.#.#.#.#.#.#.#.#.#", 
 "#.#.#.#.#.#.#.#.#.#."}

Returns: 200

A big checkerboard.

```
{"...#...#...#"}
```
```
Returns: 3
```

{".",
 "#",
 ".",
 ".",
 "#",
 "."}

Returns: 3

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