Consider a state space where the start state is the number 1 and each state has two successors: the numbers 2 and 2 + 1. (The space is a binary tree.) a. Draw the portion of the state space for states 1 to 15. b. Suppose the goal state is 11. List the order in which nodes will be visited for breadth-first search. If you are faced with any ties during the search, visit the node labeled with the lowest number firstin other words, if it would be correct to visit either node 3 or node 4 next, visit node 3 first. c. Suppose the goal state is 11. List the order in which nodes will be visited for depth-limited search with a limit of 3, using the same tie breaker as above. d. Suppose the goal state is 11. List the order in which nodes will be visited for iterative deepening search, using the same tie breaker as above. e. How well would bidirectional search work on this problem? What is the branching factor in each direction of the bidirectional search? f. Does the answer to (e) above suggest a reformulation of the problem that would allow you to solve the problem of getting from state 1 to a given goal state with almost no search?