(e) The Stable Match problem is concerned with matching n members of one set A = {an, ... , an} with n members of a set B = {b1, ..., bn}, according to a set of preferences. The aim is to produce a stable and perfect match. An algorithm to solve this problem is presented below (the Gale and Shapley algorithm we studied in our class). Initialise each element in A and B to be free While an element from A is free and has elements in B still to propose to Choose an element a from A Let b be the next best option b e B from a's preference list If b is free Match a and b Else if b prefers a to b's existing match denoted bcurrent Match a and b and set beurrent to be free Else b rejects a Explain what the complexity classes are for the best and worst case running time for this algorithm. You answer should include a diagram to illustrate one example each of the conditions where the best and worst case would occur. Each diagram should show the sets A and B, their preferences and the final match pairings produced by the algorithm. Use a size for sets A and B of 3 in your diagrams. [10 marks]