Problem 2: Search [16 Points] Suppose that you need to find a path between S and G in the following graph. The number attached to each edge in the graph represents the actual cost of traversing the edge. F 2 H S. 5 8 00 D 2 3 3 G goal Assume also that the heuristic distances to the goal from each node are given by the following table: Node SACDF G H Heuristic dist. to G 10 5 4 3 4 0 2 For each of the following search methods, list the nodes in the order in which they are expanded by the search method while looking for a solution. Show your work (the search tree and the states of the stack/queue). When everything else is equal, order the nodes in alphabetical order. i. Depth First Search ii. Uniform Cost Search iii. Greedy Best First Search iv. A* search