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Consider a state space where the start state is number 1 and each state $k$ has two successors: numbers $2k$ and $2k+1$.

  1. Draw the portion of the state space for states 1 to 15.

  2. Suppose the goal state is 11. List the order in which nodes will be visited for breadth-first search, depth-limited search with limit 3, and iterative deepening search.

  3. How well would bidirectional search work on this problem? What is the branching factor in each direction of the bidirectional search?

  4. Does the answer to (c) 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?

  5. Call the action going from $k$ to $2k$ Left, and the action going to $2k+1$ Right. Can you find an algorithm that outputs the solution to this problem without any search at all?