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Following statement is true or false?
If we make following changes to Dijkstra, then it can be used to find the longest simple path, assume that the graph is acyclic.
1) Initialize all distances as minus infinite instead of plus infinite.
2) Modify the relax condition in Dijkstra's algorithm to update distance of an adjacent v of the currently considered vertex u only if "dist[u]+graph[u][v] > dist[v]". In shortest path algo, the sign is opposite.
  • a)
    True
  • b)
    False
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Following statement is true or false?If we make following changes to D...
In shortest path algo, we pick the minimum distance vertex from the set of vertices for which distance is not finalized yet. And we finalize the distance of the minimum distance vertex. For maximum distance problem, we cannot finalize the distance because there can be a longer path through not yet finalized vertices.
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Most Upvoted Answer
Following statement is true or false?If we make following changes to D...
Explanation:

False

Reasoning:
- Dijkstra's algorithm is designed to find the shortest path in a graph, not the longest path.
- By initializing all distances as minus infinite and updating the distances based on the modified relax condition, the algorithm will not guarantee finding the longest simple path.
- The relax condition in Dijkstra's algorithm is crucial for ensuring the shortest path by comparing the current distance to a node with the sum of the distance to that node from another node and the edge weight between them. Changing this condition will not work effectively for finding the longest path in an acyclic graph.
- To find the longest simple path in an acyclic graph, other algorithms like topological sorting or dynamic programming can be more suitable.
- Therefore, making the mentioned changes to Dijkstra's algorithm will not result in finding the longest simple path in an acyclic graph.
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Following statement is true or false?If we make following changes to Dijkstra, then it can be used to find the longest simple path, assume that the graph is acyclic.1) Initialize all distances as minus infinite instead of plus infinite.2) Modify the relax condition in Dijkstra's algorithm to update distance of an adjacent v of the currently considered vertex u only if "dist[u]+graph[u][v] > dist[v]". In shortest path algo, the sign is opposite.a)Trueb)FalseCorrect answer is option 'B'. Can you explain this answer?
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