Consider the following statements about Bellman ford algorithm for fin...
Statement 1 is true as in the nth iteration of Bellman Ford, if the length of the path of any node reachable from the source is decreased, that means we are having negative edge weight cycle in the graph. Statement 2 is false as no algorithm can give give correct answer if the Graph is having negative edge weight cycle.
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Consider the following statements about Bellman ford algorithm for fin...
Understanding the Bellman-Ford Algorithm
The Bellman-Ford algorithm is designed to find the shortest paths from a source vertex to all other vertices in a directed graph, even when negative weights are present.
Statement I: Negative Edge Weight Cycle Detection
- The algorithm can indeed detect negative weight cycles that are reachable from the source vertex.
- If a negative weight cycle exists, after |V| - 1 iterations (where V is the number of vertices), the algorithm will perform an additional iteration and update distances, indicating a cycle.
- Thus, Statement I is true.
Statement II: Correctness of Shortest Path Calculation
- Although Bellman-Ford can handle negative weights, it fails to provide correct shortest path results when negative cycles are reachable from the source.
- If the shortest path includes a negative cycle, the distance can be decreased indefinitely by traversing the cycle repeatedly.
- Therefore, the algorithm does not always guarantee a correct shortest path in the presence of negative cycles.
- Hence, Statement II is false.
Conclusion
- Since Statement I is true and Statement II is false, the correct option is C: Statement I is true and Statement II is false.
This analysis highlights the strengths and limitations of the Bellman-Ford algorithm, ensuring a clear understanding of its functionality in the context of negative cycles.
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