Bucket Sort: A Comprehensive Guide
Introduction to Bucket Sort Bucket sort, sometimes referred to as bin sort, is a distribution sort algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm or recursively applying the bucket sort algorithm. Bucket sort is mainly...
NanoNeuron: The Fundamentals of Machine Learning
Machine learning has become one of the hottest topics in the tech world. However, understanding the intricacies of algorithms, networks, and layers can be quite daunting. Enter the NanoNeuron: a simplistic model consisting of seven straightforward JavaScript functions that highlight the magic behind machines’ ability to learn. Through...
Square Root Calculation: Newton’s Method
Introduction The task of computing the square root of a number is one of the classic challenges in mathematics. Over the centuries, numerous algorithms and techniques have been developed to tackle this problem, with one of the most famous being Newton’s method. This iterative numerical approach is renowned for its efficiency and precision....
Integer Partition: A Comprehensive Guide
When you think of partitions, you might imagine dividing a space into separate sections. However, in the world of mathematics, integer partition holds an entirely different meaning, one that dives deep into the composition of numbers. Definition of Integer Partition An integer partition of a number, n, is a way of expressing n as a...
Fast Powering in JavaScript: A Deep Dive
Computing the power of a number can be a straightforward task when dealing with small exponents. However, with larger values, it’s essential to implement more efficient algorithms to achieve quick results without significant computational strain. One such algorithm is the Fast Powering Algorithm. In this article, we’ll dissect this...
Sieve of Eratosthenes: An Efficient Prime Number Discovery
The Sieve of Eratosthenes is one of the most ancient algorithms known to history and remains one of the most efficient ways to find all prime numbers up to a specified integer. Historical Context Eratosthenes was a Greek mathematician, geographer, and astronomer who lived from 276 BC to 194 BC. Despite the many hats he...
Least Common Multiple (LCM): A Comprehensive Guide
The Least Common Multiple (LCM) of two integers is the smallest integer that is divisible by both of them without leaving a remainder. It’s a fundamental concept in number theory and arithmetic. This article will dive into its significance, its relation with the Greatest Common Divisor (GCD), and methods to compute it. Importance of Least...
Euclidean Algorithm: Calculating the Greatest Common Divisor
The Euclidean Algorithm is a time-tested technique, tracing back to ancient Greece, designed to compute the Greatest Common Divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers also divides their difference. Understanding the GCD The GCD of two numbers is the largest number that can exactly divide...
Primality Test: Understanding the Trial Division Method
In number theory, the Primality Test is pivotal — it discerns whether a number is prime. Among the various techniques for this test, the Trial Division Method stands out for its simplicity. What is a Prime Number? Before diving into the algorithm, let’s reiterate what a prime number is. A prime number is a natural...
The Knight’s Tour: A Classic Chessboard Challenge
The Knight’s Tour is a fascinating problem from the domain of computer science and mathematics, specifically within the realm of graph theory. The problem presents a curious challenge: Can a knight traverse every square of a chessboard exactly once? The Knight’s Tour Statement On a given N x N chessboard, determine if a knight can...