Consider the following variation of the coin change problem. You are given coin denominations x1, x2, ..., xn. You are given only one of each type of coin. You are also given a value V. Your goal is to find the maximum number of coins which will add up to value of exactly V. If it is not possible to find a set of coins with total exactly V, then the answer should be 0. To solve this, use Dynamic Programming. Define L[v,i] to be the maximum number of coins of types 1...i that can add up to value v. Now define L[v,i] in terms of previous subproblems, and give an algorithm for solving this problem which runs in time O(nv) Consider the following variation of the coin change problem. You are given coin denominations x1, x2, ..., xn. You are given only one of each type of coin. You are also given a value V. Your goal is to find the maximum number of coins which will add up to value of exactly V. If it is not possible to find a set of coins with total exactly V, then the answer should be 0. To solve this, use Dynamic Programming. Define L[v,i] to be the maximum number of coins of types 1...i that can add up to value v. Now define L[v,i] in terms of previous subproblems, and give an algorithm for solving this problem which runs in time O(nv)