I have the following question in my midterm review:
Suppose that you were planning to run A* on a unit-cost domain (ie. where all actions have a cost of 1), with a heuristic function that only returned non- negative integer values. Further, assume that you expect all optimal solutions to cost no more than 100. In no more than 6 sentences, identify an upper bound on the number of unique f-costs that the search may encounter, and justify your answer.
The way I see it, if the optimal solution does not cost more than 100, then at a maximum, it costs 100. Since all actions have a cost of 1, and we assume the optimal solution costs 100, then it must have started at start_node with a g-cost of 0, but what could the upper bound be on the h-cost? We are not told whether the heuristic function is admissible or not, so how do I know that it's not wildly over-/under-estimating the h-cost? This makes me think the f-cost can vary infinitely. Where am I going wrong?
