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board coloring, C/C++ Programming

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in this problem u given a board in which some of the elements are placed as shown in diagram below .each element represent a color .fill the other elements in the board such that none of the adjacent element shud be of the same color find out the minimum number of colors that shud b used to fill the blank spaces in the board so that the above condition is met
diagram:
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15

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