0.5 Figure 1: Shortest path problem Consider a shortest path problem as shown in figure 1 The destination is node T. The links are undirected, the cost are equal in both directions and are shown along the connecting line segments. For example, 9k(1,(1,4)) = 9k (4. (4,1)) = 6. We want to find a shortest path from each i to node T, i.e., a sequence of moves that minimizes total cost to get to destination T from each of the nodes 1,...,4. We formulate the problem as one where we require exactly N = 4 moves(stages) to reach the destination but allow degenerate moves from a node i to itself with cost gri,i,1)) = 0. For N = 4, we have JN(T) = 0, and for node i = 1,...,4,k=0,...,N-1, Ji (i) = optimal cost of getting from i to T in N - k moves. (1) Formulate this problem into a DP problem ,write down the Bellman Equation and calculate value Ji (i) for i = 1, ...,N.k=0, ...,N-1, where N = 4 in this problem. (2)Based on the results from (1), show the shortest paths from each note to the destination T. 0.5 Figure 1: Shortest path problem Consider a shortest path problem as shown in figure 1 The destination is node T. The links are undirected, the cost are equal in both directions and are shown along the connecting line segments. For example, 9k(1,(1,4)) = 9k (4. (4,1)) = 6. We want to find a shortest path from each i to node T, i.e., a sequence of moves that minimizes total cost to get to destination T from each of the nodes 1,...,4. We formulate the problem as one where we require exactly N = 4 moves(stages) to reach the destination but allow degenerate moves from a node i to itself with cost gri,i,1)) = 0. For N = 4, we have JN(T) = 0, and for node i = 1,...,4,k=0,...,N-1, Ji (i) = optimal cost of getting from i to T in N - k moves. (1) Formulate this problem into a DP problem ,write down the Bellman Equation and calculate value Ji (i) for i = 1, ...,N.k=0, ...,N-1, where N = 4 in this problem. (2)Based on the results from (1), show the shortest paths from each note to the destination T