Consider the graph below. You start at point A and wish to reach point B, only going downward at each step. When traveling an edge, you must pay the toll value associated with it. You wish to compute a path from A to B whose total cost is as small as possible. 42 32 The general problem is as follows: you are given a directed acyclic graph (DAG) with n vertices (named 1,2,... ,n), and a list of m edges (u, v) where u x, (r, y This guarantees that there is a path from the first node to the last node. (a) Consider the following local search algorithm for this problem: start at vertex 1 and always traverse down the edge with the lowest possible cost until reaching n. What total cost will this algorithm yield for the above map? Is it optimal? rithm is O(2"), as a function of the number of vertices n. and find its runtime as a function of m and n using big-O notation (b) Describe a naive algorithm for this problem such that the time complexity of this algo- c) Describe a dynamic-programming algorithm to solve this problem. Prove its correctness