Im a little lost on prob 3 can you determine the recursive formula with a brief explanation

il trom the first house to the ith Whtamed in the ith house is denoted as v When the thief reaches the ith house, he has two choices: to steal or Define F(i) for the following cases (a) Provide F(0) and F(1). Then provide F() in terms of previously computed values of F Problem 2: Summing Integers Suppose you are given a collection As {ai, a2, An} of n positive integers that add up to 2Z Design an O(nZ) time algorithm to decide if the set can be partitioned into two groups B and A B such that: a,EB E(A-B) Problem 3: Longest Paths Given an undirected graph G (V,E) with positive edge weights we for each dynamic programming algorithm to compute the longest path in G from a given source s that contains at most n edges (Hint: Let Alo, k] denote the weight of the longest path from s to node v of at most k edges)