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Is the following statement valid?.
Given a graph where all edges have positive weights, the shortest paths produced by Dijsktra and Bellman Ford algorithm may be different but path weight would always be same.
Given a graph where all edges have positive weights, the shortest paths produced by Dijsktra and Bellman Ford algorithm may be different but path weight would always be same.
- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Is the following statement valid?.Given a graph where all edges have p...
Dijkstra and Bellman-Ford both work fine for a graph with all positive weights, but they are different algorithms and may pick different edges for shortest paths.
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Is the following statement valid?.Given a graph where all edges have p...
Explanation:
Both Dijkstra and Bellman Ford algorithms are used to find the shortest path between two vertices in a graph with positive weights. However, there are some differences between both algorithms.
Dijkstra Algorithm:
The Dijkstra algorithm is a greedy algorithm that works by finding the shortest path from the starting vertex to all other vertices in the graph. It uses a priority queue to keep track of the vertices and their distances from the starting vertex. The algorithm selects the vertex with the smallest distance and updates the distances of its neighbors.
Bellman Ford Algorithm:
The Bellman Ford algorithm is a dynamic programming algorithm that works by finding the shortest path from the starting vertex to all other vertices in the graph. It uses a relaxation technique to update the distances of each vertex iteratively. The algorithm performs V-1 iterations, where V is the number of vertices in the graph.
Shortest Paths:
Both algorithms produce the shortest paths between two vertices in a graph with positive weights. However, the paths may be different due to the order in which the vertices are visited. This is because the Dijkstra algorithm uses a priority queue to select the vertex with the smallest distance, while the Bellman Ford algorithm iterates over all vertices in each iteration.
Path Weight:
Given a graph where all edges have positive weights, the shortest paths produced by both Dijkstra and Bellman Ford algorithms may be different, but the path weight would always be the same. This is because both algorithms use the same weights to calculate the shortest path. Therefore, the path weight would be the same for both algorithms.
Conclusion:
In conclusion, the statement "Given a graph where all edges have positive weights, the shortest paths produced by Dijkstra and Bellman Ford algorithm may be different, but the path weight would always be the same" is true.
Both Dijkstra and Bellman Ford algorithms are used to find the shortest path between two vertices in a graph with positive weights. However, there are some differences between both algorithms.
Dijkstra Algorithm:
The Dijkstra algorithm is a greedy algorithm that works by finding the shortest path from the starting vertex to all other vertices in the graph. It uses a priority queue to keep track of the vertices and their distances from the starting vertex. The algorithm selects the vertex with the smallest distance and updates the distances of its neighbors.
Bellman Ford Algorithm:
The Bellman Ford algorithm is a dynamic programming algorithm that works by finding the shortest path from the starting vertex to all other vertices in the graph. It uses a relaxation technique to update the distances of each vertex iteratively. The algorithm performs V-1 iterations, where V is the number of vertices in the graph.
Shortest Paths:
Both algorithms produce the shortest paths between two vertices in a graph with positive weights. However, the paths may be different due to the order in which the vertices are visited. This is because the Dijkstra algorithm uses a priority queue to select the vertex with the smallest distance, while the Bellman Ford algorithm iterates over all vertices in each iteration.
Path Weight:
Given a graph where all edges have positive weights, the shortest paths produced by both Dijkstra and Bellman Ford algorithms may be different, but the path weight would always be the same. This is because both algorithms use the same weights to calculate the shortest path. Therefore, the path weight would be the same for both algorithms.
Conclusion:
In conclusion, the statement "Given a graph where all edges have positive weights, the shortest paths produced by Dijkstra and Bellman Ford algorithm may be different, but the path weight would always be the same" is true.
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Is the following statement valid?.Given a graph where all edges have positive weights, the shortest paths produced by Dijsktra and Bellman Ford algorithm may be different but path weight would always be same.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?
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