GATE CS 2025 Set 2 — Question 59
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Programming & Data Structures → Graphs (Data Structure) → BFS Traversal
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Question
Consider the following algorithm 
someAlgo that takes an undirected graph as input.someAlgo(G)1.Let be any vertex in . Run BFS on starting at . Let be a vertex in at maximum distance from as given by the BFS.
2.Run BFS on again with as the starting vertex. Let be the vertex at maximum distance from as given by the BFS.
3.Output the distance between and in .
The output of someAlgo(T) for the tree shown in the given figure is ___________. (Answer in integer)Correct answer
6 to 6
Solution
The algorithm
someAlgo(G) is a standard two-pass Breadth-First Search (BFS) algorithm used to find the diameter of a tree. 1.Step 1: Starting from an arbitrary node , the first BFS finds a node that is at the maximum distance from . In a tree, this node is guaranteed to be one of the endpoints of a longest path (diameter).
2.Step 2: The second BFS starts from node and finds the node that is farthest from it. The distance between and is the diameter of the tree.
3.Analysis of the given tree :
- Let's identify the central node (the node with degree 4). Let's call it .
- Top branch: Path from to the top-most leaf is . This path has 3 edges.
- Bottom branch: Path from to the bottom-most leaf is . This path has 3 edges.
- Left branch: Path from to any of its 3 leaves is . This path has 2 edges.
- Right branch: Path from to any of its 2 leaves is . This path has 2 edges.
5.Diameter = Distance() + Distance() = .
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