Decision vs. Optimization

[5 marks] Suppose you have a polynomial time algorithm for the following decision problem: Given a list n numbers, al'a2, , d by S {1, , n), is there a partition S = AUB with An B = such that EA a,-EBai. Show that you can use this algorithm to find such a partition A, B (if it exists) in polynomial time. If the original algorithm runs in time O(nP), give a bound on the run time of your algorithm. an. 1ndexe