Exercises
Multiple Choice
Articles
Open Problems
Login
5 items
Topic:
Randomized Algorithms
x
Start over
- to expand, or dig in by adding more tags and revising the query.
Sort By:
trending ▼
date
0
Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Randomized QuickSort
Consider Randomized-Quicksort operating on a sequence of \(n\) distinct input numbers. Prove that the expected running time of Randomized-Quicksort is \(O(n{\log}n)\) Prove that for any constant …
Computer Science
Algorithms
Randomized Algorithms
expectation
sorting
0
Graduate
By
Shiva Kintali
on June 10, 2012 | Updated Dec. 6, 2017
Card shuffling using pairwise-swapping
You are given a deck of \(n\) cards. In each step you select two cards independently and uniformly at random and swap their positions. This defines a random walk on the set of all permutations of the …
Computer Science
Randomized Algorithms
canonical paths
coupling
random walk
0
Undergraduate
By
Shiva Kintali
on July 21, 2012 | Updated Dec. 6, 2017
Linear time shuffling
Consider the following algorithm to shuffle an array \(A\) of \(n\) elements (with indices from \(0\) to \(n-1\) : for \(i = 0\) to \(n - 1\) Let j be a random integer between 0 and i exchange A…
Computer Science
Randomized Algorithms
linear time algorithms
0
Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Generating random numbers
You are given a fair coin that comes up with heads (or tails) with probability 1/2. Using this fair coin, implement a random number generator \(Random(a,b)\) that returns an integer between \(a\) and …
Computer Science
Randomized Algorithms
generator
0
Undergraduate
By
Shiva Kintali
on June 6, 2012 | Updated Dec. 6, 2017
Reservoir Sampling
You are watching a stream of packets go by one at a time, and want to take a random sample of \(k\) distinct packets from the stream. You only have room to save \(k\) packets at any one time. You do…
Computer Science
Randomized Algorithms
sampling
icon
Sign In or Sign Up
icon
Invite Friends
Post Something
x
Select What You'd Like To Post
POST AN ARTICLE
POST AN OPEN PROBLEM
POST AN EXERCISE
POST A MULTIPLE-CHOICE QUESTION
Content Types
Articles
Open Problems
Exercises
Multiple-Choice Questions
Levels
High school
Undergraduate
Graduate
Subjects
Mathematics
Computer Science
Puzzles
Optimization
Trending tags
linear equations
primes
counting
conditional probability
interview question
vertex cover
math puzzle
expectation
basics
fibonacci
Topics
Algebra
Algorithms
Approximation Algorithms
Calculus
Combinatorial Optimization
Combinatorics
Complexity Theory
Data Structures
Discrete Mathematics
Game Theory
Geometry
Graph Theory
Linear Algebra
Linear Programming
Logic
Mathematical Analysis
Mathematics
Matrix Theory
Number Theory
Optimization
Probability
Programming
Puzzles
Randomized Algorithms
Real Analysis
Trigonometry
×