Consider the problem: given an undirected graph and a, , c, b is there a simple path from a to c that goes via b. Make every undirected edge into two anti parallel edges each with capacity 1 each. Add a source s and a directed edge of capacity 2 from s to b. Add a sink t and two directed edges from a, c into t each with capacity 1. Explain how the maximum flow answers the question above about if a simple path from a to c via b exists. Can you do the same algorithm for checking for a, b, c in a directed graph if there is a directed path from a to c that goes via b? If yes show how, else explain why not. In all algorithm, always explain how and why they work. ALWAYS, analyze the time complexity of your algorithm