Randomized Algorithms

Randomized algorithm use randomness in their computations to achieve a desired outcome. By incorporating random choices into their processes, randomized algorithms can often provide faster solutions or better approximations compared to deterministic algorithms.

• Randomized algorithms are mainly classified into Las Vegas and Monte Carlo types.
• Las Vegas algorithms always produce correct results but with variable running time. Examples are Randomized Quick Sort and Random search
• Monte Carlo algorithms have bounded running time but may produce incorrect results with a small probability. Examples are Fermat Method for Primality Testing and Randomized Karger's Algorithm

Introduction

• Introduction and Analysis
• Classification and Applications

Easy Problems

• Generates one of 3 according to given probabilities
• Generate 0 and 1 with 25% and 75% probability
• Implement rand3() using rand2()
• Birthday Paradox
• Expected Value of an array
• Shuffle a deck of cards
• Generate CAPTCHA and verify
• Index of max occurring with equal probability
• Randomized Binary Search

Medium Problems

• Make a fair coin from a biased coin
• Shuffle a given array using Fisher–Yates shuffle Algorithm
• Expected Number of Trials until Success
• Strong Password Suggester
• QuickSort using Random Pivoting
• Operations on Sparse Matrices
• Estimating the value of Pi using Monte Carlo
• Implement rand12() using rand6() in one line

Hard Problems

• Generate integer from 1 to 7
• Implement random-0-6-Generator using the given random-0-1-Generator
• Random number from stream, with O(1) space
• Random number generator in arbitrary probability distribution fashion
• Reservoir Sampling
• Linearity of Expectation
• Introduction and implementation of Karger’s algorithm for Minimum Cut
• Random Node from a Linked List
• Random Node from a tree
• Freivald’s Algorithm to check if a matrix is product of two
• Random Acyclic Maze Generator

Recommended:

• DSA Tutorial