Board Coloring

Problem Description

In this problem you are given a board in which some of the elements are placed as shown in diagram below. Each element represents a color.
Fill the other elements in the board, such that none of the adjacent elements (vertically, horizontally and diagonally) should be of the same color.
Find out the minimum number of colors that should be used to fill the blank spaces in the board, so that the above condition is met.
Color representation is -: 0, 1, 2, 3, 4, 5, 6, 7.........................
There is sample board:

            For Example:

Given Board :

Matrix representation of board is :
[ _ 1 _ _ ]
[ 2 _ _ _ ]
[ _ _ 2 _ ]
[ 2 _ _ _ ]
here blank space is represented by '_' .
Minimum colors to fill this board (given in the picture)is 4.

Instruction to work with Open PBT Client:

1. Specify the work directory path in the 'Work directory Path' field. The path should correspond to your solution Work directory.
2. Download the support files by clicking the Get Dev Files.
3. You will find the problem directories containing:
   • problem.h file
   • problem.c file

in your project directory.

1. Code the solution in.c file inside the problem directory
2. All required files will be downloaded to your work directory. Creating additional files is strongly discouraged.

Step 1:

In your Solution File:

• Implement your logic in function int color(char board[4][4])

• char   board[4][4]board is 2 dimensional matrix of order M X M where M = 4.

• You can create more functions if required, but those functions should be in the same file.

Step 2:

In your solution keep in mind the following constraints.

1. In this problem you have to write a program that finds the minimum number of colors needed to fill a board in which some of the elements are placed in advance.
2. Function color() will take 2 dimension board as a input.
3. Function color() returns the minimum number of colors that could fill the board meeting the given condition.
4. Board is a 2 dimensional of M X M where M = 4 else return 0
5. Fill the other elements in the board, such that none of the adjacent elements (vertically, horizontally and diagonally) should be of the same color.

The Prototype of the function is

int color(char board[4][4])
This function takes following arguments.

• board is 2 dimensional matrix of order M X M where M = 4.

• This function returns minimum no of color by which board can be filled.

The constraints are:

1. Board is a 2 dimensional of M X M where M = 4 else return 0
2. Fill the other elements in the board, such that none of the adjacent elements (vertically, horizontally and diagonally) should be of the same color.

Example 1

Input

{ 2 0 _ 1 }
{ _ 1 _ _ }
{ _ 2 _ 0 }
{ _ _ _ 1 }

Output

5
Explanation:
We need a minimum 5 different colors to complete the board.

Example 2

Input

{ 2 0 _ 1 3}
{ _ 1 _ _ 2}
{ _ 2 _ 0 1}
{ _ _ _ 1 2}
{ _ _ _ _ 0}

Output

0


Explanation:
Size of the board is greater than 4X4.

Example 3

Input

{ _ 0 }
{ 1 _ }

Output

0


Explanation:
Size of the board is less than 4X4.

For C solutions

For C++ solutions

General Instructions