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A* search algorithm

The algorithm is widely used in path-finding and graph traversal problems. It is an extension of Edsger Dijkstra's algorithm (1959). A* achieves better performance (with respect to time) by using heuristic function.


Peter Hart, Nils Nilsson and Bertram Raphael of Stanford Research Institute (now SRI International) described the algorithm in 1968.

It is a best-search first algorithm (best-search first alg. is estimating the promise of node n by a function f(n) tha is actually "heuristic evaluation function" f(n), so f(n) = h(n) ).

A* algorithm uses f(n) as well but it consits of two parts:

1. cost function to the node = known distance from the starting node to the current node 'n' - usually denoted g(n)

2. a future path-cost, which is an admissible "heuristic estimate" of the distance from the current node 'n' to the goal - usually denoted h(n)

Then f(n) = g(n) + h(n)



The demo below demonstrates how A* algorithm works. There are 2 grey rectangles. The left one is the start position and the right one is the position we want to get. Obviously there are also obstacles between them so the algorithm has to find the way around them.




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