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Graduate
By
Shiva Kintali
on June 17, 2012 | Updated Dec. 6, 2017
Vertex cover using DFS
Consider the following algorithm for Vertex Cover of a graph \(G\) : Run depth first search (DFS) on \(G\). Output the vertices which are not leaves in the DFS tree. Prove the following : The ou…
Computer Science
Mathematics
Approximation Algorithms
Graph Theory
vertex cover
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High School
By
Shiva Kintali
on Aug. 20, 2013 | Updated Jan. 4, 2018
Bug in a cube
A bug is sitting in one corner of a cube-shaped room. What is the shortest path to go to the extreme opposite corner (i.e., the corner that is farthest) ?
Puzzles
Puzzles
geometry puzzle
interview question
0
High School
By
Shiva Kintali
on April 1, 2014 | Updated Dec. 6, 2017
Designing two dice
You are given two blank dice i.e., all the sides of the dice are blank. You are allowed to write any integers on the sides of the dice. Only one integer on each side. Write the integers such that …
Puzzles
Puzzles
interview question
math puzzle
0
High School
By
Shiva Kintali
on May 7, 2014 | Updated Jan. 4, 2018
Sock Drawer puzzle
There are 10 socks of each of the following colors in a drawer: red blue green black white i.e., there are 50 socks. The socks are arbitrarily distributed in the drawer. You are blind-f…
Puzzles
Puzzles
math puzzle
pigeonhole principle
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Undergraduate
By
123forman
on May 8, 2014 | Updated Dec. 6, 2017
Democratic distribution of wealth
A crew of 100 pirates have captured 100 laptops. The pirates are ranked 1 through 100, with pirate 100 being the pirate king. Captured booty is distributed as follows. The pirate king proposes a dis…
Mathematics
Discrete Mathematics
Game Theory
induction
0
Undergraduate
By
Shiva Kintali
on June 7, 2012 | Updated Dec. 6, 2017
Caterpillars are Graceful
Graceful Labeling : Label the vertices of a simple undirected graph \(G(V,E)\) (where \(|V| = n\) and \(|E| = m\)) with integers from \(0\) to \(m\). Now label each edge with the absolute difference o…
Mathematics
Graph Theory
graph labeling
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Graduate
By
Shiva Kintali
on Aug. 29, 2012 | Updated Dec. 6, 2017
Random Intervals
There are \(n\) points on a line. These points are paired up at random to form \(n/2\) intervals. Prove that the probability that among these intervals there is one which intersects all the others i…
Mathematics
Puzzles
Probability
Puzzles
counting
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Undergraduate
By
Shiva Kintali
on May 31, 2012 | Updated Dec. 6, 2017
Party Problem
Suppose there are six people at a party. Prove that there are always three of them so that every two know each other (or) no two know each other. In other words, let the edges of the complete graph o…
Mathematics
Puzzles
Combinatorics
Graph Theory
Puzzles
counting
extremal graph theory
interview question
0
High School
By
Shiva Kintali
on June 28, 2012 | Updated Dec. 6, 2017
Integral Rectangles
A large rectangle is partitioned into smaller rectangles, each of which has either integer height or integer width or both. Prove that the large rectangle also has this property.
Mathematics
Puzzles
Geometry
Puzzles
interview question
math puzzle
0
Undergraduate
By
Shiva Kintali
on June 8, 2012 | Updated Dec. 6, 2017
Linear time algorithms on trees
Let \(T(V,E)\) be a tree. Design linear time (i.e., \(O(|V|)\) time) algorithms for the following problems : Find an optimal vertex cover in \(T\). Find a maximum matching in \(T\). Find a maximum i…
Computer Science
Mathematics
Algorithms
Graph Theory
independent set
linear time algorithms
matching
trees
vertex cover
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