Can you explain the Bellman-Ford algorithm with examples?
Sure! The Bellman-Ford algorithm is used to find the shortest path from a single source vertex to all other vertices in a weighted graph. It can handle graphs with negative weight edges.
Can you give me a simple example of how it works?
Absolutely! Let's say we have a graph with vertices A, B, C, and D. The edges are A->B (4), A->C (1), B->C (3), and C->D (2). Starting from A, the algorithm will update the shortest paths to each vertex.
What would the shortest path from A to D be?
The shortest path from A to D would be A -> C -> D, with a total weight of 3 (1 from A to C and 2 from C to D).
Are there any limitations of the Bellman-Ford algorithm?
Yes, the Bellman-Ford algorithm is less efficient than Dijkstra's algorithm for graphs without negative weights, as it has a time complexity of O(VE), where V is the number of vertices and E is the number of edges.
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