What are the differences between the Dijkstra Algorithm and the A* Lite Algorithm?

The Dijkstra Algorithm and the A* Lite Algorithm are both popular algorithms used for finding the shortest path in a graph. However, there are several key differences between these two algorithms.

1. Objective:
- Dijkstra Algorithm: The main objective of the Dijkstra Algorithm is to find the shortest path from a single source node to all other nodes in the graph. It does not consider any specific destination node.
- A* Lite Algorithm: The A* Lite Algorithm, on the other hand, is designed to find the shortest path from a single source node to a specific destination node in the graph. It takes into account the destination node while searching for the optimal path.

2. Heuristic Function:
- Dijkstra Algorithm: The Dijkstra Algorithm does not use any heuristic function. It relies solely on the actual cost of reaching each node from the source node.
- A* Lite Algorithm: The A* Lite Algorithm incorporates a heuristic function, typically an admissible heuristic, to guide the search towards the destination node. This heuristic function estimates the cost from the current node to the destination node, which helps in making informed decisions during the search process.

3. Memory Usage:
- Dijkstra Algorithm: The Dijkstra Algorithm maintains a priority queue or a min-heap to store the nodes and their corresponding costs. This can result in higher memory usage, especially for large graphs.
- A* Lite Algorithm: The A* Lite Algorithm also uses a priority queue or a min-heap to store the nodes, but it additionally considers the estimated cost to the destination node. This can lead to more efficient memory usage compared to Dijkstra Algorithm, as it prioritizes nodes that are closer to the destination.

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 is because it explores all the vertices and edges in the graph.
- A* Lite Algorithm: The time complexity of the A* Lite Algorithm depends on the quality of the heuristic function used. In the worst case, it can be as high as O((V + E) log V), but with a good heuristic function, it can often be significantly faster than Dijkstra Algorithm.

5. Optimality:
- Dijkstra Algorithm: The Dijkstra Algorithm guarantees to find the shortest path from the source node to all other nodes in the graph. However, it does not consider the destination node explicitly.
- A* Lite Algorithm: The A* Lite Algorithm also guarantees to find the shortest path from the source node to the destination node. By incorporating the heuristic function, it can often find the optimal path more efficiently than Dijkstra Algorithm.

In summary, the Dijkstra Algorithm and the A* Lite Algorithm differ in their objectives, use of heuristic function, memory usage, time complexity, and optimality. The Dijkstra Algorithm is suitable for finding the shortest path from a single source to all other nodes, while the A* Lite Algorithm is more focused on finding the shortest path from a single source to a specific destination.