Understanding the A* Algorithm (A Star Algorithm)
1. Principles of the A* Search Algorithm
A* algorithm is an extension of the traditional breadth-first search (BFS) or Dijkstra's algorithm. While BFS and Dijkstra's algorithm use a greedy approach based on the cost function
A* incorporates a heuristic function
h(v) to form a greedy approach based on the total cost function
f(v) = g(v) + h(v).
In fact, BFS and Dijkstra's algorithm can be seen as special cases of the
A* search algorithm, where
h(v) is always zero.
2. Efficiency of the A* Algorithm
It is difficult to achieve a perfect (correct & efficient) heuristic function
h(v). However, by incorporating some prior assumptions about the problem at hand, we can introduce a certain bias in the search order, making
A* faster than BFS or Dijkstra's algorithm in most cases.
The following animated GIF provides a visual representation:
From this GIF, we can observe the following:
- Due to the bias introduced by the heuristic function,
A*is generally faster than BFS, but only by a small margin (typically searching only half of the nodes).
- In the worst-case scenario,
A*performs similarly to BFS.
In conclusion, the
A* algorithm combines the benefits of a heuristic function with a greedy search approach, allowing for efficient pathfinding in many scenarios. However, the effectiveness of
A* heavily relies on the quality of the heuristic function employed.