Consider the 8-puzzle problem.

a. What is the maximum branching factor for this problem

b. Assume that for this problem goal state occurs at the depth 5. If depth-first search algorithm is used to solve this problem, what would be the maximum number (worst-case) of time steps that depth-first algorithm takes to find the goal state.

c. Assume that for this problem goal state occurs at the depth k . If depth-first search algorithm is used to solve this problem, estimate the space complexity of this search algorithm.