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 greedy best-first search strategies. It evaluates nodes based on a combination of the actual cost from the source node and the estimated cost to the goal node using the heuristic function. This evaluation helps prioritize nodes that are more likely to lead to the goal, resulting in a more efficient search.

3. Heuristic Function:
- Dijkstra Algorithm: Dijkstra Algorithm does not utilize any heuristic function. It only considers the actual cost of reaching each node from the source node.
- A* Algorithm: A* Algorithm incorporates a heuristic function that provides an estimate of the remaining distance from the current node to the goal. This heuristic helps guide the search towards the goal, making it more efficient by reducing the number of unnecessary explorations.

4. Time Complexity:
- Dijkstra Algorithm: The time complexity of the Dijkstra Algorithm is O((V + E) log V), where V is the number of vertices and E is the number of edges in the graph. This complexity arises due to the use of a priority queue to efficiently select the next node with the minimum distance.
- A* Algorithm: The time complexity of the A* Algorithm depends on the heuristic function used. In the worst case, it can be exponential. However, with an admissible and consistent heuristic, the time complexity is often much lower than the worst case.

In summary, the main differences between the Dijkstra Algorithm and the A* Algorithm lie in their objectives, search strategies, incorporation of heuristic functions, and time complexities. While Dijkstra Algorithm guarantees finding the shortest path, A* Algorithm is more efficient in many cases due to its heuristic-guided search strategy.