Dijkstra's A* Algorithm in plain english

dijkstras-a-star-plain-english.md

Dijkstra's (A*) Algorithm in plain English

Inputs: A graph or grid where each node represents a location and has associated costs, and a start node and a goal node.

Goal: Find the shortest path from the start node to the goal node while considering the associated costs and heuristics.

1. Initialize Open and Closed Sets:

   • Create an open set containing the start node. This set represents nodes to be evaluated.
   • Create an empty closed set. This set represents nodes that have already been evaluated.

2. Main Loop:

   • While the open set is not empty:
     • Choose the node from the open set with the lowest combined cost f(n) = g(n) + h(n), where g(n) is the cost to reach the current node and h(n) is a heuristic estimate of the cost to reach the goal.
     • If the chosen node is the goal node, the path has been found. Construct the path by following parent pointers from the goal node to the start node.
     • Move the chosen node from the open set to the closed set.

3. Expand Node and Update Open Set:

   • For each neighboring node of the chosen node:
     • If the node is in the closed set, skip it.
     • If the node is not in the open set, add it to the open set and set its parent pointer to the chosen node.
     • If the node is already in the open set, calculate the tentative g score (cost to reach the current node). If the tentative score is lower than the existing score, update the node's parent and g score.

4. Heuristics:

   • The choice of heuristic h(n) affects the efficiency of the A* algorithm. A good heuristic should provide an optimistic estimate of the remaining cost from the current node to the goal. Common heuristics include Euclidean distance, Manhattan distance, and octile distance.

5. Result:

   • If the open set becomes empty and the goal node is not reached, no path exists from the start node to the goal node.

Advantages:

• A* is guaranteed to find the shortest path if the heuristic is admissible (never overestimates the true cost) and consistent (satisfies the triangle inequality).
• The use of heuristics allows A* to focus on promising paths and avoid exploring unpromising ones.

Limitations:

• A* can be memory-intensive if there are many nodes in the open set.
• The efficiency of A* heavily depends on the quality of the heuristic. An inaccurate heuristic can lead to suboptimal paths.

The A* algorithm is widely used in pathfinding and graph traversal problems where finding the shortest path is crucial.