We’re asked to the captain of the uci’s tennis team to arrange a series of matches against long beach state’s team3 . both teams have n players; the tennis rating (a positive number, where a higher number can be interpreted to mean a better player) of the ith member of uci’s team is ai and the tennis rating for the kth member of lbsu’s team is sk. we would like to set up a competition in which each person plays one match against a player from the opposite school. because we get to select who plays against whom, our goal is to make sure that in as many matches as possible, the uci player has a higher tennis rating than their opponent. give an efficient greedy algorithm for this problem and prove that it is correct (maximizes the number of wins our team achieves).