Problem 2 In the same tree search problem, suppose that we have selected a heuristic given by the following table. Sate Heuristic A 5 BCDEFGHIK 42 1 10 11 4 1 a) Is this an admissible heuristic? Why or why not? b) Using Uniform Cost Search (UCS) algorithm, write the ordered in which the nodes are expanded in addition to the value of the expansion criterion (e.g., cost) used to decide which node to expand. (Use alphabetical order to break ties). Also write the search solution reached by this al Order of node expansion Value of expansion criterion 1 2 3 4 5 6 Order of node expansion A B D F Value of expansion criterion Start state 1 2 2 18 9 10 11 12 Search solution: A Order of mode expansion Value of expansion criterion c) Repeat (b) for Greedy search. # Order of node Value of expansion expansion criterion 1 A Start state 2 B 4 3 D 2 4 F 2 5 6 Search solution: A 7 8 9 10 11 12 Order of node expansion Value of expansion criterion d) Repeat (b) for A* search. Order of node expansion 1 A 2 B 3 D 4 F 5 6 Search solution: A Value of expansion criterion Start state 1 2 2 7 8 19 10 11 12 e) Is the following an admissible heuristic? Why or why not? Sate E F G H Heuristic 5 4 2 5 1 1 0 2 1 2