1. Graded Problem (Page limit: 1 sheet; 2 sides) A bandit has broken into a store and has found many items he wants to bring with him and then flee the scene. There are n items, of positive integer sizes s1,82,... , Sn. Each item has a positive value to him, vi, v2,..., vn. Being greedy the bandit would have liked to bring everything, but for the fact that his getaway car has only a limited capacity that can hold a total size at most S. Therefore his problem is to select a subset A { 1, 2, . . . , n} such that the sum EA Si S and the total value (his total loot) U. iEA is maximized. Find a Dynamic Programming algorithm to solve this problem. Your solution should have worst case running time polynomial in s1,82,... , STn, v1, v2,... , Vn, and S Analyze its running time. Prove your algorithm is correct, and runs in your stated time. Hint: Suppose his total capacity is S - 1?) 1. Graded Problem (Page limit: 1 sheet; 2 sides) A bandit has broken into a store and has found many items he wants to bring with him and then flee the scene. There are n items, of positive integer sizes s1,82,... , Sn. Each item has a positive value to him, vi, v2,..., vn. Being greedy the bandit would have liked to bring everything, but for the fact that his getaway car has only a limited capacity that can hold a total size at most S. Therefore his problem is to select a subset A { 1, 2, . . . , n} such that the sum EA Si S and the total value (his total loot) U. iEA is maximized. Find a Dynamic Programming algorithm to solve this problem. Your solution should have worst case running time polynomial in s1,82,... , STn, v1, v2,... , Vn, and S Analyze its running time. Prove your algorithm is correct, and runs in your stated time. Hint: Suppose his total capacity is S - 1?)