You are given a set of n points (zi, yi) for i = 1.2, , n respectively corresponding to cities c1, c2, cy, , cn in the Euclidean plane. The travel distance between any pair of cities is the Euclidean distance between the corresponding points. City ci located at (xi, /i) is your home city. The Traveling Salesperson Problem (TSP) seeks to find a Hamiltonian cycle (or, "tour") over the n cities (i.e., a closed path that begins and ends at your home city c1, and that visits every other city exactly once) that has minimum total travel distance. Consider the following "greedy" approach to finding a low-cost tour over the n cities: Initialize all cities to "unvisited Set current-city = C1; mark c1 as "visited". . For j=1, . .. , n-1: Travel from current.city to the nearest city, city nert, that is "unvisited" - Mark city.nert as "visited". Set current.city = city.next Travel from current.city to ci (a) Show that this "greedy" approach to TSP is not optimal by exhibiting a small counterexample. (b) How badly suboptimal do you think the greedy approach can be, relative to optimal? Please clearly explain your definition of "badly suboptimal