Open In App

Randomized Algorithms

Last Updated : 22 Feb, 2024
Like Article

Randomized algorithms in data structures and algorithms (DSA) are algorithms that use randomness in their computations to achieve a desired outcome. These algorithms introduce randomness to improve efficiency or simplify the algorithm design. By incorporating random choices into their processes, randomized algorithms can often provide faster solutions or better approximations compared to deterministic algorithms. They are particularly useful in situations where exact solutions are difficult to find or when a probabilistic approach is acceptable.

For example, in Randomized Quick Sort, we use a random number to pick the next pivot (or we randomly shuffle the array). Typically, this randomness is used to reduce time complexity or space complexity in other standard algorithms.

Introduction to Randomized Algorithms:

Easy Problems on Randomized Algorithms:

Medium Problems on Randomized Algorithms:

Hard Problems on Randomized Algorithms:


Previous Article
Next Article

Similar Reads

Importance of Randomized Algorithms
Introduction: Randomization is an important concept, and hence randomization algorithms are used in a variety of fields, such as number theory, computational geometry, graph theory, and distributed computing.The inputs for a randomized algorithm are similar to those of deterministic algorithms, along with a sequence of random bits that can be used
4 min read
Randomized Algorithms | Set 1 (Introduction and Analysis)
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 Randomized Quick Sort, we use a random number to pick the next pivot (or we randomly shuffle the array). And in Karger's algorithm, we randomly pick an edge. How to analyse Randomize
6 min read
Randomized Algorithms | Set 2 (Classification and Applications)
We strongly recommend to refer below post as a prerequisite of this. Randomized Algorithms | Set 1 (Introduction and Analysis) Classification Randomized algorithms are classified in two categories. Las Vegas: A Las Vegas algorithm were introduced by Laszlo Babai in 1979. A Las Vegas algorithm is an algorithm which uses randomness, but gives guarant
13 min read
Randomized Algorithms | Set 3 (1/2 Approximate Median)
We strongly recommend to refer below articles as a prerequisite of this. Randomized Algorithms | Set 1 (Introduction and Analysis) Randomized Algorithms | Set 2 (Classification and Applications) In this post, a Monte Carlo algorithm is discussed. Problem Statement : Given an unsorted array A[] of n numbers and ε > 0, compute an element w
4 min read
Randomized Algorithms | Set 0 (Mathematical Background)
Conditional Probability Conditional probability P(A | B) indicates the probability of even 'A' happening given that the even B happened.[Tex]P(A|B) = \frac{P(A\cap B)}{P(B)} [/Tex]We can easily understand above formula using below diagram. Since B has already happened, the sample space reduces to B. So the probability of A happening becomes P(A ? B
3 min read
Count of array elements that can be found using Randomized Binary Search on every array element
Given an array arr[] of size N, the task is to find the minimum count of array elements found by applying the Randomized Binary Search for each array elements. Examples: Input: arr[] = { 5, 4, 9 } Output: 2 Explanation: Applying Randomized Binary Search for arr[0] in the array. Initially, search space is [0, 2] Suppose pivot = 1 and arr[pivot] <
7 min read
Disjoint Set Union (Randomized Algorithm)
A Disjoint set union is an algorithm that is used to manage a collection of disjoint sets. A disjoint set is a set in which the elements are not in any other set. Also, known as union-find or merge-find. The disjoint set union algorithm allows you to perform the following operations efficiently: Find: Determine which set a given element belongs to.
15+ min read
Load Balancing on Servers (Randomized Algorithm)
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 requests. How should the load be balanced among servers? The solutions that we generally think of are a) Round Robin b) Assign new request to a server that has minimum load. Both of t
3 min read
Treap (A Randomized Binary Search Tree)
Like Red-Black and AVL Trees, Treap is a Balanced Binary Search Tree, but not guaranteed to have height as O(Log n). The idea is to use Randomization and Binary Heap property to maintain balance with high probability. The expected time complexity of search, insert and delete is O(Log n). Every node of Treap maintains two values. 1) Key Follows stan
2 min read
Randomized Binary Search Algorithm
We are given a sorted array A[] of n elements. We need to find if x is present in A or not.In binary search we always used middle element, here we will randomly pick one element in given range.In Binary Search we had middle = (start + end)/2 In Randomized binary search we do following Generate a random number t Since range of number in which we wan
13 min read
Article Tags :
Practice Tags :