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A* Search - artificial intelligence:
A* search in the combines is the best parts of uniform cost search, namely the fact that it's optimal and complete, and the other best parts of greedy search, namely its speed. This kind of searching strategy simply combines the path cost function g(n) and the heuristic function h(n) by summing them to form a new heuristic measure f(n):
f(n) = g(n) + h(n)
Remembering that g(n) gives the path cost from the start state to state n and h(n) estimates the path cost from n to a goal state, we see that f(n) estimates the cost of the cheapest solution that passes through n.
The most important aspect of A* search is that, given only one restriction on h(n), it is possible to prove the search strategy there which is complete and optimal. The restriction to h(n) is that it must all the time underestimate the cost to reach a goal state from n. Such heuristic measures are called admissible. Look at Russell and Norvig for proof that A* search with an admissible heuristic is complete and optimal.
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