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Provide an algorithm with time complexity analysis to solve the following problem:Determine if a given map with n "countries" can be legally 3-colored. Assume that you can check.Note: By definition, a map can be legally k-colored if and only if there exists a way to color all of the countries using up to k different colors in such a way that no two adjacent countries have the same color. One of the most famous results in Math/CS states that any map can be 4-colored.
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