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Consider the following statements about Dijkstra’s algorithm.
1. Dijkstra’s algorithm produces an incorrect result only if the graph contains a negative weight cycle.
2. If a graph contains a negative weight cycle, then Dijkstra's algorithm may not terminate.
Which of the above statements is true?
- a)Only 1
- b)Only 2
- c)Both 1 & 2
- d)None
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following statements about Dijkstra’s algorithm.1. ...
Dijkstra’s algorithm may produce incorrect result even if does not contain a negative weight cycle.
Example:
The distance of C is 3 by Dijkstra's algorithm.
2. Dijkstra’s algorithm always terminates after |V| iterations.
Most Upvoted Answer
Consider the following statements about Dijkstra’s algorithm.1. ...
Incorrect Result and Negative Weight Cycle
Dijkstra's algorithm is a popular algorithm for finding the shortest path from a starting node to all other nodes in a graph with non-negative edge weights.
- Statement 1 is true as Dijkstra's algorithm produces incorrect results when the graph contains a negative weight cycle. This is because the algorithm assumes that all edge weights are non-negative, and the presence of a negative weight cycle can cause the algorithm to produce incorrect shortest path distances.
Negative Weight Cycle and Termination
- Statement 2 is also true as if a graph contains a negative weight cycle, Dijkstra's algorithm may not terminate. This is because the algorithm greedily selects the node with the smallest distance as the next node to explore, and in the presence of a negative weight cycle, it can get stuck in an infinite loop trying to reduce the distance by repeatedly traversing the negative weight cycle.
- As a result, the algorithm may not terminate and fail to find the correct shortest paths in the presence of such cycles.
Conclusion
- Therefore, both statements are true, highlighting the limitations of Dijkstra's algorithm when dealing with graphs that contain negative weight cycles. It is important to preprocess the graph to detect and handle negative weight cycles before applying Dijkstra's algorithm to ensure correct results and termination.
Dijkstra's algorithm is a popular algorithm for finding the shortest path from a starting node to all other nodes in a graph with non-negative edge weights.
- Statement 1 is true as Dijkstra's algorithm produces incorrect results when the graph contains a negative weight cycle. This is because the algorithm assumes that all edge weights are non-negative, and the presence of a negative weight cycle can cause the algorithm to produce incorrect shortest path distances.
Negative Weight Cycle and Termination
- Statement 2 is also true as if a graph contains a negative weight cycle, Dijkstra's algorithm may not terminate. This is because the algorithm greedily selects the node with the smallest distance as the next node to explore, and in the presence of a negative weight cycle, it can get stuck in an infinite loop trying to reduce the distance by repeatedly traversing the negative weight cycle.
- As a result, the algorithm may not terminate and fail to find the correct shortest paths in the presence of such cycles.
Conclusion
- Therefore, both statements are true, highlighting the limitations of Dijkstra's algorithm when dealing with graphs that contain negative weight cycles. It is important to preprocess the graph to detect and handle negative weight cycles before applying Dijkstra's algorithm to ensure correct results and termination.
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Consider the following statements about Dijkstra’s algorithm.1. Dijkstra’s algorithm produces an incorrect result only if the graph contains a negative weight cycle.2. If a graph contains a negative weight cycle, then Dijkstra's algorithm may not terminate.Which of the above statements is true?a)Only 1b)Only 2c)Both 1 & 2d)NoneCorrect answer is option 'D'. Can you explain this answer?
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