Statement for Linked Answer Questions 80 and 81: The subset-sum problem is…

Statement for Linked Answer Questions 80 and 81: The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a₁, a₂, a₃, …, aₙ}, and a positive integer W, is there a subset of S whose elements sum to W? A dynamic program uses a 2-dimensional Boolean array X with n rows and W+1 columns. X[i,j], 1 ≤ i ≤ n, 0 ≤ j ≤ W, is TRUE if and only if a subset of {a₁,…,aᵢ} sums to j.

Question 81: Which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?