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DSA / Algorithms / Randomized

Randomized

40 posts

Binomial Random Variables

Last Updated: 23 July 2025

In this post, we'll discuss Binomial Random Variables.Prerequisite : Random Variables A specific type of discrete random variable that counts how often a particular event ...read more

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Find an index of maximum occurring element with equal probability

Last Updated: 16 March 2023

Given an array of integers, find the most occurring element of the array and return any one of its indexes randomly with equal probability.Examples:Input: arr[] = [-1, 4, ...read more

Implement rand12() using rand6() in one line

Last Updated: 08 July 2024

Given a function, rand6() that returns random numbers from 1 to 6 with equal probability, implement the one-liner function rand12() using rand6() which returns random numb...read more

Implement rand3() using rand2()

Last Updated: 09 June 2022

Given a function rand2() that returns 0 or 1 with equal probability, implement rand3() using rand2() that returns 0, 1 or 2 with equal probability. Minimize the number of ...read more

Generate 0 and 1 with 25% and 75% probability

Last Updated: 01 July 2022

Given a function rand50() that returns 0 or 1 with equal probability, write a function that returns 1 with 75% probability and 0 with 25% probability using rand50() only. ...read more

Randomized Algorithms | Set 0 (Mathematical Background)

Last Updated: 23 July 2025

Conditional Probability Conditional probability P(A | B) indicates the probability of even 'A' happening given that the even B happened.P(A|B) = \frac{P(A\cap B)}{P(B)}We ...read more

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Randomized Algorithms | Set 3 (1/2 Approximate Median)

Last Updated: 23 July 2025

Time Complexity:We use a set provided by the STL in C++. In STL Set, insertion for each element takes O(log k). So for k insertions, time taken is O (k log k).Now replacin...read more

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statistical-algorithms

Fermat Method of Primality Test

Last Updated: 23 July 2025

Given a number n, check if it is prime or not. We have introduced and discussed the School method for primality testing in Set 1.Introduction to Primality Test and School ...read more

Modular Arithmetic

Randomized Algorithms | Set 2 (Classification and Applications)

Last Updated: 23 July 2025

We strongly recommend to refer below post as a prerequisite of this. Randomized Algorithms | Set 1 (Introduction and Analysis)ClassificationRandomized algorithms are class...read more

Randomized Algorithms | Set 1 (Introduction and Analysis)

Last Updated: 23 July 2025

What is a Randomized Algorithm?An algorithm that uses random numbers to decide what to do next anywhere in its logic is called a Randomized Algorithm. For example, in Rand...read more

Analysis and applications Karger’s algorithm for Minimum Cut

Last Updated: 23 July 2025

We have introduced and discussed below Karger's algorithm in set 1.1) Initialize contracted graph CG as copy of original graph2) While there are more than 2 vertices. ...read more

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Select a Random Node from a Singly Linked List

Last Updated: 23 July 2025

Given a singly linked list, select a random node from the linked list (the probability of picking a node should be 1/N if there are N nodes in the list). You are given a r...read more

Introduction and implementation of Karger's algorithm for Minimum Cut

Last Updated: 23 July 2025

Given an undirected and unweighted graph, find the smallest cut (smallest number of edges that disconnects the graph into two components). The input graph may have paralle...read more

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graph-connectivity

Load Balancing on Servers (Randomized Algorithm)

Last Updated: 23 July 2025

Consider a high traffic website that receives millions of requests (of different types) per five minutes, the site has k (for example n = 1000) servers to process the requ...read more

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Expected Number of Trials until Success

Last Updated: 23 July 2025

Consider the following famous puzzle.In a country, all families want a boy. They keep having babies till a boy is born. What is the expected ratio of boys and girls in the...read more

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harmonic progression