Consistent Hashing



Video Lectures on Discrete Mathematics and Algorithms

Stony Brook  [my Alma Mater 🙂 ]

IMSc (Indian Institute of Mathematical Sciences):


Finding two largest elements in an array

This is a very interesting problem indeed.

The problem comes in multiple flavors:

  • Find two largest elements in an array in 1.5n comparisons.
  • Find two largest elements in an array in n+log(n)−2 comparisons.
  • Prove that no algorithm for finding two largest elements in an array can do this in less than n+ log (n)−2 comparisons.
  • What is the fastest algorithm for finding three largest elements?




Alias method

“You are given an n-sided die where side i has probability pi of being rolled. What is the most efficient data structure for simulating rolls of the die?”

A very similar question was posted to me recently  :

The approaches above are very cool, and illustrate the use of augmented search trees.

However, it seems there is a better method for this problem – and it has been out there for a while now. This was a fascinating read :

Additional pointers for the alias method:



Bentley’s Treatment of the Maximum Sum Subsequence Problem

I thoroughly enjoyed the treatment given to this problem by Jon Bentley.

In particular, the section on “Principles” was such an exciting read – it shows some of the tricks used in algorithm design :

  • Save state to avoid recomputation
  • Preprocess state into data structures 
  • Divide and conquer algorithms
  • Scanning algorithms
  • Cumulatives 
  • Lower bounds
  • Sorting (my humble addition to the list)