Discussion on Greedy Search and A*. Best-first search. Idea: use an evaluation function f(n) for each node estimate of "desirability" Expand most desirable unexpanded node Implementation : Order the nodes in fringe in decreasing order of desirability Special cases:
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Order the nodes in fringe in decreasing order of desirability
h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n.
Proof by Contradiction:
Hence f(G2) > f(n), and A* will never select G2 for expansion; Contradiction: Algorithm would have not terminated at G2 and expanded n instead because f(n)<f(G)f(G2)
h(n) ≤ c(n,a,n') + h(n')
f(n') = g(n') + h(n')
= g(n) + c(n,a,n') + h(n')
≥ g(n) + h(n)
E.g., for the 8-puzzle:
(i.e., no. of squares from desired location of each tile)