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Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights. Statement I: It will always find out negative edge weight cycle in G reachable from source. Statement II: It will always give correct answer for the graph G. Choose from the options given below.
- a)Both statements are true
- b)Both statements are false
- c)Statement I is true and Statement II is false
- d)Statement II is true and Statement I is false
Correct answer is option 'C'. Can you explain this answer?
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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...
Statement I: It will always find out negative edge weight cycle in G reachable from source.
The Bellman-Ford algorithm is used to find the shortest path from a source vertex to all other vertices in a directed connected graph. It can handle graphs with negative edge weights but not negative cycles.
To understand why Statement I is true, we need to understand the concept of negative cycles. A negative cycle is a cycle in a graph where the sum of the weights of the edges along the cycle is negative.
The Bellman-Ford algorithm works by relaxing all the edges in the graph repeatedly. In each iteration, it updates the distance of every vertex from the source by considering all the edges. If after V-1 iterations, where V is the number of vertices in the graph, there is still a possibility to update the distance, then there exists a negative cycle reachable from the source.
The reason behind this is that in any shortest path, the maximum number of edges is V-1. If there is a negative cycle reachable from the source, then we can keep going around the cycle to decrease the distance infinitely. After V-1 iterations, if we can still update the distance, it means that there is a negative cycle reachable from the source.
Therefore, Statement I is true. The Bellman-Ford algorithm will always find out a negative edge weight cycle in G if it is reachable from the source.
Statement II: It will always give correct answer for the graph G.
The Bellman-Ford algorithm is guaranteed to give the correct answer for the shortest path problem if the graph does not contain any negative cycles reachable from the source.
The algorithm iterates V-1 times, where V is the number of vertices in the graph. In each iteration, it relaxes all the edges in the graph, updating the distance of every vertex from the source. This process ensures that the shortest path distances are correctly calculated for all vertices that are reachable from the source.
However, if the graph contains a negative cycle, the algorithm will not give the correct answer. This is because a negative cycle allows for infinite decreases in the distance, and the algorithm will keep updating the distances infinitely.
Therefore, Statement II is false. The Bellman-Ford algorithm will not always give the correct answer for the graph G if it contains a negative cycle reachable from the source.
Conclusion
In conclusion, Statement I is true as the Bellman-Ford algorithm will always find out a negative edge weight cycle in G if it is reachable from the source. However, Statement II is false as the algorithm will not always give the correct answer for the graph G if it contains a negative cycle reachable from the source.
The Bellman-Ford algorithm is used to find the shortest path from a source vertex to all other vertices in a directed connected graph. It can handle graphs with negative edge weights but not negative cycles.
To understand why Statement I is true, we need to understand the concept of negative cycles. A negative cycle is a cycle in a graph where the sum of the weights of the edges along the cycle is negative.
The Bellman-Ford algorithm works by relaxing all the edges in the graph repeatedly. In each iteration, it updates the distance of every vertex from the source by considering all the edges. If after V-1 iterations, where V is the number of vertices in the graph, there is still a possibility to update the distance, then there exists a negative cycle reachable from the source.
The reason behind this is that in any shortest path, the maximum number of edges is V-1. If there is a negative cycle reachable from the source, then we can keep going around the cycle to decrease the distance infinitely. After V-1 iterations, if we can still update the distance, it means that there is a negative cycle reachable from the source.
Therefore, Statement I is true. The Bellman-Ford algorithm will always find out a negative edge weight cycle in G if it is reachable from the source.
Statement II: It will always give correct answer for the graph G.
The Bellman-Ford algorithm is guaranteed to give the correct answer for the shortest path problem if the graph does not contain any negative cycles reachable from the source.
The algorithm iterates V-1 times, where V is the number of vertices in the graph. In each iteration, it relaxes all the edges in the graph, updating the distance of every vertex from the source. This process ensures that the shortest path distances are correctly calculated for all vertices that are reachable from the source.
However, if the graph contains a negative cycle, the algorithm will not give the correct answer. This is because a negative cycle allows for infinite decreases in the distance, and the algorithm will keep updating the distances infinitely.
Therefore, Statement II is false. The Bellman-Ford algorithm will not always give the correct answer for the graph G if it contains a negative cycle reachable from the source.
Conclusion
In conclusion, Statement I is true as the Bellman-Ford algorithm will always find out a negative edge weight cycle in G if it is reachable from the source. However, Statement II is false as the algorithm will not always give the correct answer for the graph G if it contains a negative cycle reachable from the source.
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Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer?
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Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer?.
Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about Bellman ford algorithm for finding shortest path in a directed connected graph G having integral edge weights.Statement I:It will always find out negative edge weight cycle in G reachable from source.Statement II:It will always give correct answer for the graph G.Choose from the options given below.a)Both statements are trueb)Both statements are falsec)Statement I is true and Statement II is falsed)Statement II is true and Statement I is falseCorrect answer is option 'C'. Can you explain this answer?.
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