Problems 1. You are given an unlimited number of coins consisting of nickels (5 cents) dimes (10 cents) and quarters (25 cents). Your task is to get 30 cents with as few coins as possible. This problem can be described as search, where the decision in each level of the search tree is what coin to choose next. The first two levels of the search tree are shown below, where a left branch indicates a choice of a nickel (5 cents) a center branch indicates the choice of a dime, and a right branch indicates the choice of a quarter. The number written in each node is the total amount. o (1). Let Vbe the value in oden. Define the heuristic h(n) to be (30 - Viif in 30 If best first search is applied to the entire tree) with this heuristic, the solution found would have nickels (5 cents each), dimes (10 cents each), and quarters (25 cents each). (2). How much memory would be used by best first search?__ (3). Prove that the heuristic h(n) is not admissible. Can you suggest a nontrivial (e.g. not always 0) admissible heuristic for this problem? Problems 1. You are given an unlimited number of coins consisting of nickels (5 cents) dimes (10 cents) and quarters (25 cents). Your task is to get 30 cents with as few coins as possible. This problem can be described as search, where the decision in each level of the search tree is what coin to choose next. The first two levels of the search tree are shown below, where a left branch indicates a choice of a nickel (5 cents) a center branch indicates the choice of a dime, and a right branch indicates the choice of a quarter. The number written in each node is the total amount. o (1). Let Vbe the value in oden. Define the heuristic h(n) to be (30 - Viif in 30 If best first search is applied to the entire tree) with this heuristic, the solution found would have nickels (5 cents each), dimes (10 cents each), and quarters (25 cents each). (2). How much memory would be used by best first search?__ (3). Prove that the heuristic h(n) is not admissible. Can you suggest a nontrivial (e.g. not always 0) admissible heuristic for this