Consider the following algorithm someAlgo that takes an undirected graph $ G $ as input. someAlgo(G) Let $ v $ be any vertex in $ G $. 1. Run BFS on $ G $ starting at $ v $. Let $ u $ be a vertex in $ G $ at maximum distance from $ v $ as given by the BFS. 2. Run BFS on $ G $ again with $ u $ as the starting vertex. Let $ z $ be the vertex at maximum distance from $ u $ as given by the BFS. 3. Output the distance between $ u $ and $ z $ in $ G $. The output of tt{someAlgo(T)} for the tree shown in the given figure is ____________ . (Answer in integer)

Question

Consider the following algorithm someAlgo that takes an undirected graph $ G $ as input.  someAlgo(G) Let $ v $ be any vertex in $ G $.  1. Run BFS on $ G $ starting at $ v $. Let $ u $ be a vertex in $ G $ at maximum distance from $ v $ as given by the BFS.  2. Run BFS on $ G $ again with $ u $ as the starting vertex. Let $ z $ be the vertex at maximum distance from $ u $ as given by the BFS. 3. Output the distance between $ u $ and $ z $ in $ G $.  The output of tt{someAlgo(T)} for the tree shown in the given figure is ____________ . (Answer in integer)

cdquestions Admin · Accepted Answer

The algorithm tt{someAlgo} effectively finds the diameter of the tree $ T $, which is the longest shortest path between any two nodes in the tree. Step 1: Run BFS from any arbitrary node $ v $ - Select an arbitrary node and perform a BFS to find the farthest node $ u $.  Step 2: Run BFS from $ u $ to find the farthest node $ z $ - Perform another BFS starting from $ u $ to determine the farthest node $ z $. Step 3: Compute the distance between $ u $ and $ z $ - The distance obtained in this second BFS represents the tree's diameter. From the given tree diagram, the longest shortest path (diameter) is found to be $ 6 $.

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