CubeNets | Topcoder Archive

Problem Statement

In geometry a cube net is an arrangement of identical edge-joined squares in the plane which can be folded (along the edges) to become the faces of a cube.

In this problem you need to check if the given figure is a cube net. The given figure will be a union of six identical squares lying in the same plane and will be given to you as a String[] figure. Each element of figure will consist of '.' (dot) and '#' (sharp) characters only. A sharp represents one of the six squares, whereas a dot represents an empty space. Return "YES" if figure represents a cube net, or "NO" otherwise (all quotes for clarity).

Definition

Class:: CubeNets
Method:: isCubeNet
Parameters:: String[]
Returns:: String
Method signature:: String isCubeNet(String[] figure)
(be sure your method is public)

Constraints

figure will contain between 1 and 6 elements, inclusive.
Each element of figure will contain between 1 and 6 characters, inclusive.
Each element of figure will contain '.' (dot) and '#' (sharp) characters only.
All elements of figure will contain the same number of characters.
There will be exactly 6 '#' (sharp) characters among all the elements of figure.

Examples

```
{"..#.",
 "####",
 "..#."}
```
```
Returns: "YES"
```
Here you can first fold across all the vertical edges to make the middle four squares become the down, right, up and left faces of the cube-to-be. One then finishes off the construction by folding across the remaining two edges to make the other two squares become the front and back faces of the cube.
```
{"###",
 "###"}
```
```
Returns: "NO"
```
This is not a cube net.
```
{"..#.",
"####",
".#.."}
```
```
Returns: "YES"
```

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

Returns: "YES"

```
{"####",
 "...#",
 "...#"}
```
```
Returns: "NO"
```

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