Budding Scientist

Budding Scientist Interview Questions and Answers

Updated 5 Dec 2016

Q1. Graph Theory : Obtain the number of tournaments with 'N' nodes. Now define a transitive tournament as one where any three nodes (i,j,k) can be arranged in such a way that i->j->k and i->k. Define sub-tournament...

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Ans.

The aim is to find an upper bound for the minimum number of nodes in a maximal transitive sub-tournament.

  • A transitive tournament is one where any three nodes can be arranged in a way that satisfies the transitive property.

  • A sub-tournament is an induced graph on a subset of nodes from the original tournament.

  • Every tournament with N nodes contains a transitive sub-tournament of size 2 (a directed edge).

  • The goal is to find the maximal transitive sub-tournament with the minimum n...read more

Q2. An MST is constructed for a very large graph. Now, one of the edges, in the graph, has its weight altered (either increased or decreased). Now obtain the MST for the new graph using the old graphs MST and the g...

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Ans.

To obtain the MST for the new graph, we can use the old graph's MST as a starting point and update it based on the altered edge's weight.

  • Start with the old graph's MST

  • Remove the edge with the altered weight from the MST

  • Add the altered edge to the new graph

  • Run a minimum spanning tree algorithm on the new graph to obtain the updated MST

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