Combinatorics Combinatorics – Filling vacant spaces In the last article, we have tried to solve some combinatorics problems from our own intiuition. It’s all how you use multiplication and addition. We saw why n! gives us the number of ways to arrange n distinct objects. We also developed a notion of filling vacant spaces. This idea of filling January 2, 2020January 28, 2020

Combinatorics Introduction to Basic Combinatorics Combinatorics is a branch of mathematics which is about counting. Here we are concerned with problems which basically ask the total number of ways to do something. Combinatorics is just a fancy word for counting techniques. Combinatorial problems have attracted the attention of mathematicians since December 1, 2019January 23, 2020

Number Theory Prime Factorization using Sieve Method In the previous article, we’ve seen how we can calculate the prime factorization of a single number. Today, we’ll focus on how we can efficiently find factorization in a range . If you understand the sieve algorithm to find prime numbers, you’re good to go. In case you don’t October 17, 2019January 19, 2020

Number Theory The Unique Prime Factorization Theorem The fundamental theorem of arithmatic states that any number greater than 1 can be represented as a product of primes and this form of represenation is unique. Remember factoring integers in grade school? That’s exactly what we’re talking about. Now we’ll see two proofs which’ October 6, 2019January 2, 2020

Number Theory Sieve of Eratosthenes – Generate prime numbers In the last article about prime numbers, I discussed about different types of primilarity test and Trial division method to verify if a number is a prime. If you haven’t read that yet, here is the article, Prime numbers and basic primilarity test. In this article, we’ll focus on sieve of August 30, 2019February 28, 2020

Number Theory Prime numbers and basic primilarity test A prime number is a integer greater than 1 and has no positive divisors other than 1 and itself. 1 is neither prime nor composite. The set of positive integers can be divided into three classes, primes, composites and a unit (1). For example, 5 is prime because the only ways of writing it as August 14, 2019February 27, 2020

Number Theory GCD and the Euclidean Algorithm Suppose we have two integers a and b. We say that the number d is the greatest common divisor of a and b if and only if, d \mid a and d \mid b and if c \mid a and c \mid b, then c \leq d. Condition 1 says that d is a common July 13, 2019January 26, 2020

Number Theory Some interesting types of numbers and their properties Numbers are really beautiful. When you dive deep into the properties of numbers, you’ll find amazing patterns. These findings are absoulutely satisfying. It doesn’t really matter whether you need it or not. Today we’ll take a look at triangular numbers, oblong numbers, also deficie June 30, 2019December 29, 2019

CPP Arrays and vectors in C++ An array is a linear data structure which stores a collection of elements stored in contiguous memory. If you come from a JavaScript background, you might not notice the problems that I want to discuss today. I was in the same situation, when I was learning C++. I was asking myself, “Really ? November 21, 2018December 29, 2019

JavaScript Coercion in JavaScript Coercion is the phenomenon that implicitly converts a value from one primitive type to another. Many times we need to convert a particular data type to another data type. If you have programmed in C/C++ or Java, you are more likely to encounter type casting where you have to convert a variable from September 9, 2017December 29, 2019