A* Algorithm

This code implements the A* algorithm in JavaScript using p5.js, a JavaScript library for creating graphics and animations. The algorithm finds the shortest path between a start and end point on a 2D grid, taking into account the terrain (walls) between them.

Algorithm

The A* algorithm can be described in a more mathematical form as follows:

Given:

• $ G $: Graph representing the environment
• $ S $: Starting node
• $ D $: Destination node
• $ h(n) $: Heuristic function estimating the cost from node $ n $ to the destination node $ D $
• $ g(n) $: Actual cost from the starting node $ S $ to node $ n $
• $ f(n) $: Evaluation function combining $ g(n) $ and $ h(n) $, defined as $ f(n) = g(n) + h(n) $
• $ Q $: Priority queue containing nodes to be explored, ordered by $ f(n) $

Algorithm:

1. Initialize:
   • Add $ S $ to $ Q $
   • Set $ g(S) = 0 $
   • Calculate $ h(S) $ (heuristic value from $ S $ to $ D $)
   • Calculate $ f(S) = g(S) + h(S) $
2. While $ Q $ is not empty:
   • Remove the node $ n $ with the lowest $ f(n) $ from $ Q $
   • If $ n = D $, terminate (path found)
   • Add $ n $ to the set of explored nodes
   • For each neighbor $ m $ of $ n $:
     • If $ m $ is not traversable or $ m $ is in the set of explored nodes, skip to the next neighbor
     • Calculate tentative $ g(m) $ from $ S $ to $ m $
     • If $ m $ is not in $ Q $ or $ tentative , g(m) $ is less than the current $ g(m) $:
       • Update $ g(m) $ to tentative $ g(m) $
       • Calculate $ h(m) $ (heuristic value from $ m $ to $ D $)
       • Calculate $ f(m) = g(m) + h(m) $
       • Set the parent of $ m $ to $ n $
       • Add $ m $ to $ Q $
3. If the loop terminates without finding $ D $, there is no path from $ S $ to $ D $

The algorithm aims to minimize the $ f(n) $ value by considering both the actual cost $ g(n) $ and the estimated cost $ h(n) $ to reach the destination node $ D $. By iteratively exploring nodes with the lowest $ f(n) $, $A^*$ efficiently finds the shortest path from $ S $ to $ D $.

Contributing

Contributions are welcome! If you find any issues or want to add new features, feel free to submit a pull request.

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