A* search algorithm

A* is a best-first search algorithm that ranks paths by their known cost so far plus a heuristic estimate of the remaining cost to a goal.

Evaluation function: A rule that assigns a score to each candidate state or path for ordering a search. A* orders frontier paths by f(n) = g(n) + h(n), its defining evaluation rule.
Graph search: Search through vertices and edges to find states or paths satisfying a goal condition. A* is a graph-search strategy for finding a least-cost route to a goal.
Grid pathfinding: Finding a route through a grid while accounting for blocked cells and movement costs. Manhattan or diagonal-distance estimates make A* effective on many grid maps.
Breadth-first search: A graph traversal that explores states in increasing numbers of edges from the start. It finds shortest paths only when all edges have equal cost, unlike general-cost A*.
Admissible heuristic: A heuristic that never overestimates the true minimum cost from a state to a goal. Admissibility lets A* return an optimal path when its other conditions hold.
Pathfinding: The computational problem of finding a route between locations under movement rules and costs. A* is widely used to solve pathfinding problems with explicit route costs.
Navigation system: A system that computes routes between locations using a transport network and route criteria. Road-network routing can use A*-style estimates of remaining travel cost.
Depth-first search: A graph traversal that follows one branch deeply before backtracking to alternatives. It uses little frontier memory but offers no A*-like guarantee of a cheapest path.
Consistent heuristic: A heuristic satisfying the triangle inequality across every transition and equaling zero at a goal. Consistency supports efficient graph search without repeatedly reopening settled states.
Shortest path problem: The problem of finding a minimum-total-weight path between specified vertices in a graph. A* solves this problem when its heuristic and search conditions support optimality.

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