(Forward Dynamic Programming) Given a problem of finding a shortest path from node s to node t, we can obtain an equivalent "reverse" shortest path problem, where we want to find a shortest path from t to s in a graph derived from the original by reversing the direction of all the arcs, while keeping their length unchanged. Apply this transformation to the dynamic programming problem of Example 2.2 and Exercise 2.23, and derive a dynamic programming algorithm that proceeds forwards rather than backwards in time.