The most widely known form of best-first search is called A* Search.
It evaluates nodes by combining g(n), the cost to reach the node, and h(n), the cost to get from the node to the goal:
F(n) = g(n) + h(n)
Since g(n) gives the path cost from the start node to node n, and h(n) is the estimated cost of the cheapest path from n to the goal, we have:
F(n)= estimated cost of the cheapest solution through n.
Thus, if we are trying to find the cheapest solution, a reasonable thing to try first is the node with the lowest of f(n).
It turns out that this strategy is more reasonable: provided that the heuristic function h(n) satisfies certain conditions, A* search is both complete and optimal. The algorithm is identical to Uniform-cost-search exceptthat A* uses g(h) and h(n) instead of g(h).
The way of how the A* Search works is illustrated in the figure below. Each time, the node having the lowest f(n) value is the node expanded. The targets nodes will be expanded until reaching the goal destination, which is Bucharest.
