As this snippet doesn't really help a lot to know what A* search actually is, here is the explanation from Artificial Intelligence: A Modern Approach (from Russ

As this snippet doesn't really help a lot to know what A* search actually is, here is the explanation from Artificial Intelligence: A Modern Approach (from Russel and Norvig): The most widely-known form of best-first search is called A-start search (pronounced "A-star 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 value of g(n) + h(n). It turns out that this strategy is more than just reasonable: provided that the heuristic function h(n) satisfies certain conditions, K search is both complete and optimal. So, for the following graph (tree actually): +---A---+ | | B h:1 E h:4 | C h:2 | D h:3 Where the function g(x) is the depth of the node in the tree, and the heuristic function h(x) is presented next to the node (random values), A-star will search for a solution first in the nodes with smaller values of f(n). So a traversal starting at node A will visit nodes in the following order: {A, B, C, E, D} f(B) = h(B) + g(B) = 1 + 1 = 2 f(C) = 2 + 2 = 4 f(E) = 4 + 1 = 5 f(D) = 3 + 3 = 6 If there's anything wrong with my explanation please correct me. P.S.: I know my heuristic function is probably not admissible.