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
someAlgo is the two-pass BFS method for the diameter of a tree: the vertex farthest from any start vertex is always an endpoint of some longest path, so the farthest vertex from gives = diameter.Structure of the tree (14 vertices, 13 edges). Let be the central vertex of degree 4 (lower middle). Its neighbours are:- (upper left), which has three further branches: a leaf directly above-left; a vertex with two leaves (top); and a vertex with one leaf (lower left);
- (right), which has a leaf above it and a path to the far-right leaf;
- two leaves directly below .
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