Question 2: Search algorithms (Adapted from Russell & Norvig) a) Describe a state space in which iterative deepening search performs much worse than depth-first search (for example, O(n) vs O(n)). Prove each of the following statements, or give a counterexample: b) Breadth-first search is a special case of uniform-cost search. c) Uniform-cost search is a special case of A* search. d) A* search is optimal in the case where negative edge weights are allowed. e) Best-first search is optimal in the case where we have a perfect heuristic (i.e., h(n) = h*(n), the true cost to the closest goal state). f) Suppose there is a unique optimal solution. Then, A* search with a perfect heuristic will never expand nodes that are not in the path of the optimal solution. Question 2: Search algorithms (Adapted from Russell & Norvig) a) Describe a state space in which iterative deepening search performs much worse than depth-first search (for example, O(n) vs O(n)). Prove each of the following statements, or give a counterexample: b) Breadth-first search is a special case of uniform-cost search. c) Uniform-cost search is a special case of A* search. d) A* search is optimal in the case where negative edge weights are allowed. e) Best-first search is optimal in the case where we have a perfect heuristic (i.e., h(n) = h*(n), the true cost to the closest goal state). f) Suppose there is a unique optimal solution. Then, A* search with a perfect heuristic will never expand nodes that are not in the path of the optimal solution