What are the differences between Bellman-Ford and Dijkstra's algorithms?

What are the differences between Bellman-Ford and Dijkstra's algorithms?

Bellman-Ford and Dijkstra's algorithms are both used for finding the shortest paths in graphs, but they have key differences. Bellman-Ford can handle graphs with negative weight edges, while Dijkstra's algorithm cannot. Additionally, Dijkstra's is generally faster for graphs with non-negative weights.

Can you explain how each algorithm works?

Sure! Dijkstra's algorithm works by selecting the nearest vertex and updating the distances to its neighbors. It uses a priority queue for efficiency. Bellman-Ford, on the other hand, relaxes all edges repeatedly, allowing it to find the shortest paths even with negative weights, but it's slower due to its repeated edge checks.

In what scenarios would I use Bellman-Ford over Dijkstra?

You would use Bellman-Ford when your graph has negative weight edges or when you need to detect negative weight cycles. It's also useful for graphs that are not dense, as it can handle more complex scenarios.

Which algorithm is more efficient in terms of time complexity?

Dijkstra's algorithm is generally more efficient with a time complexity of O((V + E) log V) using a priority queue, while Bellman-Ford has a time complexity of O(VE). Therefore, for graphs without negative weights, Dijkstra's is preferred.