What are negative cycles in the Bellman-Ford algorithm?
An example of an AI chatbot conversation about the Bellman-Ford algorithm and negative cycles.
Can you explain what negative cycles are in the Bellman-Ford algorithm?
Negative cycles are cycles in a graph where the total weight of the edges is negative, allowing for infinite reductions in path cost.
How does the Bellman-Ford algorithm detect negative cycles?
The algorithm detects negative cycles by performing an extra iteration after the usual relaxation process. If any distance can still be updated, a negative cycle exists.
What happens if a graph has a negative cycle?
If a graph has a negative cycle, the shortest path cannot be determined, as you can keep reducing the path cost indefinitely.
Can you give an example of a negative cycle?
Sure! In a graph with vertices A, B, and C, if the edges are A->B (weight 1), B->C (weight -2), and C->A (weight 1), the cycle A->B->C->A has a total weight of 0, but can be reduced further.
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