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Board Coloring , C/C++ Programming

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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.

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