Finding the Shortest Path
Pathfinding — finding the shortest route between two points in a graph or grid — is one of the most practical problems in computer science. From GPS navigation to video game AI, from robot motion planning to network routing, the ability to efficiently find optimal paths is essential. The A* algorithm, published in 1968, remains the gold standard for informed search.
The Power of Heuristics
What makes A* special is its use of a heuristic function — an estimate of the remaining distance to the goal. This estimate guides the search toward promising directions rather than exploring blindly. Compare A* to Dijkstra (no heuristic) or BFS (uniform expansion): A* typically explores dramatically fewer nodes while finding the same optimal path. The heuristic must be admissible — it can never overestimate the true distance.
Watching the Search
The visualization shows the grid with start (green) and end (red) markers. Dark gray blocks are obstacles. As the algorithm runs, explored cells shade from dark to light blue, revealing the search frontier's expansion pattern. A* shows a focused beam toward the goal; BFS shows concentric rings; Dijkstra falls somewhere between. The final shortest path lights up in cyan.
Algorithm Comparison
BFS explores all nodes at distance d before any at distance d+1, guaranteeing optimality in unweighted graphs. Dijkstra generalizes BFS to weighted graphs. A* adds goal-directed heuristic guidance to Dijkstra. In practice, A* often explores 50-80% fewer nodes than BFS for the same grid, making it dramatically faster for real-world pathfinding applications.