1. For the following problems, describe a brute-force algorithm for solving them, and determine (an upper bound on the time complexity of your algorithm. (b) Determine if a given map with n "countries can be legally 3-colored. Assume that you can check whether any given pair of countries are neighbors of each other in O(1) time. 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