What are the differences between Floyd-Warshall and Dijkstra's algorithms?

What are the differences between Floyd-Warshall and Dijkstra's algorithms?

Floyd-Warshall is used for finding shortest paths between all pairs of vertices, while Dijkstra's algorithm finds the shortest path from a single source to all other vertices.

When should I use Floyd-Warshall instead of Dijkstra?

Use Floyd-Warshall when you need to find shortest paths between all pairs of nodes, especially in dense graphs. Dijkstra is better for sparse graphs and when you only need the shortest path from one source.

Are there any performance differences between the two?

Yes, Floyd-Warshall has a time complexity of O(V^3), making it less efficient for large graphs. Dijkstra's algorithm, with a priority queue, has a time complexity of O(E + V log V), which is generally faster for sparse graphs.

Can you give an example of when to use each algorithm?

Sure! Use Dijkstra's for GPS navigation (finding the shortest route from one location to another) and Floyd-Warshall for network routing protocols that need to know the shortest paths between all nodes.