What is the difference between the Dijkstra Algorithm and the A* Algorithm?

The Dijkstra Algorithm and the A* Algorithm are both popular algorithms used in pathfinding and graph traversal problems. While they share some similarities, there are key differences between the two.

1. Objective:
- Dijkstra Algorithm: The main objective of the Dijkstra Algorithm is to find the shortest path between a source node and all other nodes in a weighted graph. It does not consider any heuristic or estimate of the remaining distance to the goal.
- A* Algorithm: The A* Algorithm also aims to find the shortest path between a source node and a goal node in a weighted graph. However, it incorporates a heuristic function that estimates the remaining distance from the current node to the goal. This heuristic helps guide the search towards the goal, making A* more efficient in many cases.

2. Search Strategy:
- Dijkstra Algorithm: Dijkstra Algorithm uses a breadth-first search strategy, exploring nodes in a non-decreasing order of their distances from the source node. It considers all possible paths and updates the distances to each node as it progresses.
- A* Algorithm: A* Algorithm combines both breadth-first search and best-first search strategies. It uses a priority queue to explore nodes based on their estimated total cost, which is the sum of the actual cost from the source node and the heuristic estimate to the goal. This allows A* to prioritize nodes that are likely to lead to the goal, resulting in a more efficient search.

3. Memory Usage:
- Dijkstra Algorithm: Dijkstra Algorithm maintains a list of distances for all nodes in the graph, which requires storing and updating the distances for each node. This can lead to higher memory usage, especially in large graphs.
- A* Algorithm: A* Algorithm also maintains a list of distances for all nodes, similar to Dijkstra. However, it additionally stores the heuristic estimates for each node. While this increases memory usage compared to Dijkstra, the overall memory requirements are usually manageable.

4. Optimality:
- Dijkstra Algorithm: Dijkstra Algorithm guarantees finding the shortest path from the source node to all other nodes in the graph. It explores all possible paths and updates the distances until the optimal path is found.
- A* Algorithm: A* Algorithm is also guaranteed to find the shortest path from the source node to the goal node, given an admissible heuristic. However, if the heuristic is not admissible (overestimates the remaining distance), A* may not find the optimal path.

In summary, the main differences between the Dijkstra Algorithm and the A* Algorithm lie in their objectives, search strategies, memory usage, and optimality guarantees. While Dijkstra is simpler and guarantees optimality, A* is more efficient due to its heuristic-guided search and can find optimal paths with the right heuristic.