# A* search algorithm

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A* (pronounced "A-star") is a graph traversal and path search algorithm, which is used in many fields of computer science due to its completeness, optimality, and optimal efficiency.[1] One major practical drawback is its ${\displaystyle O(b^{d})}$ space complexity, as it stores all generated nodes in memory. Thus, in practical travel-routing systems, it is generally outperformed by algorithms that can pre-process the graph to attain better performance,[2] as well as memory-bounded approaches; however, A* is still the best solution in many cases.[3]

Quick facts: Class, Data structure, Worst-case performance...
Class Search algorithm Graph ${\displaystyle O(|E|log|V|)=O(b^{d})}$ ${\displaystyle O(|V|)=O(b^{d})}$
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Peter Hart, Nils Nilsson and Bertram Raphael of Stanford Research Institute (now SRI International) first published the algorithm in 1968.[4] It can be seen as an extension of Dijkstra's algorithm. A* achieves better performance by using heuristics to guide its search.

Compared to Dijkstra's algorithm, the A* algorithm only finds the shortest path from a specified source to a specified goal, and not the shortest-path tree from a specified source to all possible goals. This is a necessary trade-off for using a specific-goal-directed heuristic. For Dijkstra's algorithm, since the entire shortest-path tree is generated, every node is a goal, and there can be no specific-goal-directed heuristic.

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