# Best-first search

Best-first search is a search algorithm which explores a graph by expanding the most promising node chosen according to a specified rule.

Judea Pearl described best-first search as estimating the promise of node n by a "heuristic evaluation function ${\displaystyle f(n)}$ which, in general, may depend on the description of n, the description of the goal, the information gathered by the search up to that point, and most important, on any extra knowledge about the problem domain."[1][2]

Some authors have used "best-first search" to refer specifically to a search with a heuristic that attempts to predict how close the end of a path is to a solution, so that paths which are judged to be closer to a solution are extended first. This specific type of search is called greedy best-first search[2] or pure heuristic search.[3]

Efficient selection of the current best candidate for extension is typically implemented using a priority queue.

The A* search algorithm is an example of best-first search, as is B*. Best-first algorithms are often used for path finding in combinatorial search. (Neither A* nor B* is a greedy best-first search as they incorporate the distance from start in addition to estimated distances to the goal.)

## Greedy BFS

Using a greedy algorithm, expand the first successor of the parent. After a successor is generated:[4]

1. If the successor's heuristic is better than its parent, the successor is set at the front of the queue (with the parent reinserted directly behind it), and the loop restarts.
2. Else, the successor is inserted into the queue (in a location determined by its heuristic value). The procedure will evaluate the remaining successors (if any) of the parent.