Write down the short answer of the following. Please justify your answer with proper mathematical functions. i. Suppose you are asking to design the problem solver; this solver is used the tree structured based constraint satisfaction problem. What should be th e running time of this solver. Justify your answer with logical reasoning.
ii. suppose you are running the minimax with Alpha-beta pruning. What should be the space and time complexity of the tree with branching factor P and the depth limited Q.
iii. for uniform cost search, what effect on the path return by the search algorithm when we add some positive constant P to step cost.
iv. Suppose we have two heuristics P(S) and Q(S) for A* search. Suppose the A* is admissible for these two heuristics, when should happen with the average of these two heuristics