TopCoder problem "ColorfulTiles" used in SRM 472 (Division I Level Three)



Problem Statement

    Taro likes colorful things, especially colorful tiles.



Taro's room is an H x W rectangle divided into 1 x 1 tiles. Each tile is one of the following four colors: red, green, blue or yellow. You are given a String[] room. If the j-th character of the i-th element is 'R', 'G', 'B' or 'Y', the color of the tile in the j-th column of the i-th row is red, green, blue or yellow, respectively.



He decided to change the color of some tiles so that no two adjacent tiles have the same color. Two tiles are adjacent if they share a side or a corner (so a tile has at most 8 adjacent tiles). He is allowed to change at most K tiles.



Return the number of ways to change tiles that satisfies the above conditions, modulo 1,000,000,007. Two ways are considered to be different if there is at least one tile of distinct color.
 

Definition

    
Class:ColorfulTiles
Method:theCount
Parameters:String[], int
Returns:int
Method signature:int theCount(String[] room, int K)
(be sure your method is public)
    
 

Constraints

-room will contain between 1 and 50 elements, inclusive.
-Each element of room will contain the same number of characters.
-Each element of room will contain between 1 and 50 characters, inclusive.
-Each character in room will be 'R', 'G', 'B' or 'Y'.
-K will be between 0 and the number of characters in room, inclusive.
 

Examples

0)
    
{"RG"}
1
Returns: 5
If he doesn't change any tiles, he can make "RG".

If he changes the first tile, he can make "BG" or "YG".

If he changes the second tile, he can make "RB" or "RY".
1)
    
{"BY"}
2
Returns: 12
All pairs of different colors are possible.
2)
    
{"RG",
 "GR"}
2
Returns: 8
The eight ways are: 



RG  RG  BY  YB  BG  YG  RB  RY
BY  YB  GR  GR  YR  BR  GY  GB
3)
    
{"BRYBGYRB"
,"GRYGYBBG"
,"RGBGYBYG"
,"YRBRGBYG"
,"RBGRBRGG"
,"RBGYRYBY"}
34
Returns: 489
4)
    
{"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBBBBBBYYYYYBBBBBBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBBBYYYYYYYYYYYBBBBBBBB"
,"BBBBBBYYYYYYYYYYYYYYYYBBBBBBBBYYYYBBBBBYYYYBBBBBBB"
,"BBBBBBYYYYYYYYYYYYYYYYBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBBYYYYBBBBBYYYYBBBBBBB"
,"BBBBBBYYYBBBBBBBBBBBBBBBBBBBBBBBYYYYYYYYYBBBBBBBBB"
,"BBBBBBYYYYYYYYYYYYBBBBBBBBBBBBBBYYYYYYYYYBBBBBBBBB"
,"BBBBBBYYYYYYYYYYYYYYBBBBBBBBBBYYYYBBBBBYYYYBBBBBBB"
,"BBBBBBBBBBBBBBBBYYYYYBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBBBBBBBBBBBBBYYYBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBBBBBBBBBBBBBYYYBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBYYYBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBYYYBBBBBBBBBYYYBBBBBBBBYYYBBBBBBBBBYYYBBBBBB"
,"BBBBBBBYYYYBBBBBYYYYBBBBBBBBBBYYYYBBBBBYYYYBBBBBBB"
,"BBBBBBBBYYYYYYYYYYYBBBBBBBBBBBBYYYYYYYYYYYBBBBBBBB"
,"BBBBBBBBBBBYYYYYBBBBBBBBBBBBBBBBBBYYYYYBBBBBBBBBBB"
,"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"}
825
Returns: 404506540

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10758

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14154&pm=10758

Writer:

rng_58

Testers:

PabloGilberto , ivan_metelsky , Chmel_Tolstiy

Problem categories:

Dynamic Programming, Math