What are the complexities of Dijkstra's and A* algorithms?

What are the complexities of Dijkstra's and A* algorithms?

Dijkstra's algorithm has a time complexity of O(V^2) with a simple implementation, but can be improved to O(E + V log V) with a priority queue. A* algorithm's complexity is similar, O(E) in the worst case, but it can be more efficient with a good heuristic.

What factors affect the performance of these algorithms?

The performance of Dijkstra's and A* algorithms is affected by factors like the graph's density, the choice of data structures, and the heuristic used in A*.

Can you explain how the heuristic in A* works?

In A*, the heuristic estimates the cost from the current node to the goal. A good heuristic helps the algorithm prioritize paths that are likely to lead to the goal faster, improving efficiency.

Are there scenarios where one algorithm is preferred over the other?

Yes, A* is often preferred in pathfinding scenarios where a heuristic can be effectively applied, while Dijkstra's is used when all edge weights are non-negative and no heuristic is available.