GATE CS 2015 Set 1 — Question 51
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Algorithms → Graph Algorithms → BFS Shortest Path
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Question
Let be a simple undirected graph, and be a particular vertex in it called the source. For , let denote the shortest distance in from to . A breadth first search (BFS) is performed starting at . Let be the resultant BFS tree. If is an edge of that is not in , then which one of the following CANNOT be the value of ?
Correct answer
(D) 2
Solution
In a BFS, for any edge in the graph , the difference in shortest path distances from the source satisfies . Specifically for non-tree edges in BFS:
1.Cross edges within the same level: .
2.Cross edges between adjacent levels: or or .
An edge cannot skip a level (i.e., connect vertices with distance difference ) in BFS. Therefore, cannot be 2.Continue learning with Success Tracker
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