Recursive Definition

A partition of a positive integer n is a way to write n as a sum of positive integers. For instance, 7 = 3 + 2 + 1 + 1 is a partition of 7. Let Pm equal the number of different partions of m, where the order of the terms in the sum does not matter, and let Pm,n be the number of different ways to express m as the sum of positive integers not exceeding n. a) Show that Pm,n = Pm b) Show that the following recursive definition for Pm,n is correct: { 1 if m = 1 1 if n = 1 Pm,n = Pm.n if m < n 1 + Pm,m-1 if m = n > 1 Pm,n-1 + Pm-1,n if m > n > 1 } c) Find the number of partitions OF A NUMBER ENTERED BY THE USER (the program must prompt the user for the number) using this recursive definition. THE PROGRAM MUST ALSO, DISPLAY PARTIONS ON SCREEN. ## Deliverables 1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. 2) Complete ownership and distribution copyrights to all work purchased. 3) Must use comments. ## Platform Visual C++ 6.0