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Which of the following statement(s)is / are correct regarding Bellman-Ford shortest path algorithm?
P: Always finds a negative weighted cycle, if one exist s.
Q: Finds whether any negative weighted cycle is reachable from the source.
P: Always finds a negative weighted cycle, if one exist s.
Q: Finds whether any negative weighted cycle is reachable from the source.
- a)P Only
- b)Q Only
- c)Both P and Q
- d)Neither P nor Q
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following statement(s)is / are correct regarding Bellman-...
Bellman-Ford shortest path algorithm is a single source shortest path algorithm. So it can only find cycles which are reachable from a given source, not any negative weight cycle. Consider a disconnected where a negative weight cycle is not reachable from the source at all. If there is a negative weight cycle, then it will appear in shortest path as the negative weight cycle will always form a shorter path when iterated through the cycle again and again.
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Which of the following statement(s)is / are correct regarding Bellman-...
Bellman-Ford Shortest Path Algorithm
The Bellman-Ford algorithm is a popular algorithm used to find the shortest path between a source vertex and all other vertices in a weighted directed graph. It can handle graphs with negative weight edges, unlike Dijkstra's algorithm.
Statement P: Always finds a negative weighted cycle, if one exists.
The statement P is not correct. The Bellman-Ford algorithm is not designed to find negative weighted cycles. Its main purpose is to find the shortest path between a source vertex and all other vertices. If there is a negative weighted cycle present in the graph, the algorithm will detect it as part of its execution, but it will not provide information about the cycle itself.
The algorithm repeatedly relaxes the edges of the graph for a total of V-1 times, where V is the number of vertices in the graph. If there is a negative weighted cycle, the algorithm will continue to relax the edges indefinitely, resulting in the detection of negative cycles.
Statement Q: Finds whether any negative weighted cycle is reachable from the source.
The statement Q is correct. The Bellman-Ford algorithm can detect whether a negative weighted cycle is reachable from the source vertex. During its execution, if the algorithm relaxes an edge that leads to a shorter path, it indicates the presence of a negative cycle. This is because the negative cycle can be traversed repeatedly, resulting in an infinitely decreasing path length.
When the algorithm has completed its execution, if there are still updates being made to the distances of the vertices, it indicates the presence of a negative cycle. This information can be used to determine if a negative cycle is reachable from the source vertex.
Conclusion
In conclusion, the correct statement(s) regarding the Bellman-Ford shortest path algorithm are:
Q: Finds whether any negative weighted cycle is reachable from the source.
Therefore, option 'B' is the correct answer.
The Bellman-Ford algorithm is a popular algorithm used to find the shortest path between a source vertex and all other vertices in a weighted directed graph. It can handle graphs with negative weight edges, unlike Dijkstra's algorithm.
Statement P: Always finds a negative weighted cycle, if one exists.
The statement P is not correct. The Bellman-Ford algorithm is not designed to find negative weighted cycles. Its main purpose is to find the shortest path between a source vertex and all other vertices. If there is a negative weighted cycle present in the graph, the algorithm will detect it as part of its execution, but it will not provide information about the cycle itself.
The algorithm repeatedly relaxes the edges of the graph for a total of V-1 times, where V is the number of vertices in the graph. If there is a negative weighted cycle, the algorithm will continue to relax the edges indefinitely, resulting in the detection of negative cycles.
Statement Q: Finds whether any negative weighted cycle is reachable from the source.
The statement Q is correct. The Bellman-Ford algorithm can detect whether a negative weighted cycle is reachable from the source vertex. During its execution, if the algorithm relaxes an edge that leads to a shorter path, it indicates the presence of a negative cycle. This is because the negative cycle can be traversed repeatedly, resulting in an infinitely decreasing path length.
When the algorithm has completed its execution, if there are still updates being made to the distances of the vertices, it indicates the presence of a negative cycle. This information can be used to determine if a negative cycle is reachable from the source vertex.
Conclusion
In conclusion, the correct statement(s) regarding the Bellman-Ford shortest path algorithm are:
Q: Finds whether any negative weighted cycle is reachable from the source.
Therefore, option 'B' is the correct answer.
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