- pygame
- math
- Priority Queue
f(x) = h(x) + g(x)
h(x) = heuristic estimate function
g(x) = distance from start node and end node
A* uses this heuristic to improve on the behavior relative to Dijkstra's algorithm. When the heuristic evaluates to zero, A* is equivalent to Dijkstra's algorithm. As the heuristic estimate increases and gets closer to the true distance, A* continues to find optimal paths, but runs faster (by virtue of examining fewer nodes). When the value of the heuristic is exactly the true distance, A* examines the fewest nodes. (However, it is generally impractical to write a heuristic function that always computes the true distance, as the same comparison result can often be reached using simpler calculations – for example, using Manhattan distance over Euclidean distance in two-dimensional space.) As the value of the heuristic increases, A* examines fewer nodes but no longer guarantees an optimal path. In many applications (such as video games) this is acceptable and even desirable, in order to keep the algorithm running quickly.