Complexity
The time complexity of A* depends on the heuristic. In the worst case, the number of nodes expanded is exponential in the length of the solution (the shortest path), but it is polynomial when the search space is a tree, there is a single goal state, and the heuristic function h meets the following condition:
where is the optimal heuristic, the exact cost to get from to the goal. In other words, the error of h will not grow faster than the logarithm of the “perfect heuristic” that returns the true distance from x to the goal (see Pearl 1984 and also Russell and Norvig 2003, p. 101)
Read more about this topic: A* Search Algorithm
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