What is the time complexity of the Floyd-Warshall algorithm?

What is the time complexity of the Floyd-Warshall algorithm?

The Floyd-Warshall algorithm has a time complexity of O(V^3), where V is the number of vertices in the graph.

Can you explain why it has that complexity?

Sure! The algorithm uses three nested loops to update the shortest paths between all pairs of vertices, leading to the cubic complexity.

Are there any space complexity considerations?

Yes, the space complexity is O(V^2) because it requires a 2D array to store the shortest path distances between each pair of vertices.

How does it compare to Dijkstra's algorithm?

Dijkstra's algorithm is more efficient for sparse graphs with a time complexity of O(E + V log V), while Floyd-Warshall is better for dense graphs.

In what scenarios would you prefer Floyd-Warshall over Dijkstra's?

Floyd-Warshall is preferred when you need to find shortest paths between all pairs of vertices, especially in dense graphs.