mathematical algorithm - OpenGenus IQ

Number of arithmetic progression subsequences in a given set of numbers

The problem is that given an array of n positive integers. The task is to count the number of Arithmetic Progression subsequence in the array. This can be solved using dynamic programming in linear time complexity.

algorithm

Find the Longest Arithmetic Progression using Dynamic Programming

The problem we will solve is that given a set of integers in sorted order, find length of longest arithmetic progression in that set. This can be solved by brute force in O(N^3) while a dynamic programming approach with take O(N^2) time complexity.

game theory

Zobrist Hashing

Algorithm Complexity Implementations Applications Questions Reading time: 15 minutes | Coding time: 5 minutes Zobrist hashing (additionally alluded to as Zobrist keys or Zobrist marks ) is a hash function development utilized as a part

game theory

Alpha Beta Pruning in Minimax Algorithm

Algorithm Complexity Implementations Applications Questions Reading time: minutes | Coding time: minutes Like we discussed in earlier article, a hard coded AI can be used to create an intelligent opponent which you can challenge

game theory

Von Neumann's Minimax Theorem/ algorithm

Introduction Algorithm Complexity Implementations Applications Questions Reading time: 25 minutes | Coding time: 10 minutes Ever since the idea of artificial intelligence dawned upon the humanity, the basic concept of playing games against an

bitwise operation

Detect if a number is power of 4 using bitwise operators

Reading time: 15 minutes | Coding time: 2 minutes Algorithm Implementation Complexity Questions Bitwise operators are one of the most under-rated operators in C/C++, despite being quite fast as most of the processors

bitwise operation

Check if Two Numbers are Equal using Bitwise Operators

Bitwise Operators Explanation Implementations Applications Reading time: 15 minutes | Coding time: 2 minutes In this article, we will explore the technique of checking whether two numbers are equal using bitwise operators. Bitwise operator

bitwise operation

Detect if a number is power of 2 using bitwise operators

Reading time: 15 minutes | Coding time: 1 minutes Algorithm Implementation Complexity Questions Bitwise operators are one of the most under-rated operators in C/C++, despite being quite fast as most of the processors

game theory

Sprague-Grundy Theorem and Game of Kayle

Sprague Grundy function returns smallest non negative integer which is not in the given set. Explore the application of Sprague Grundy Theorem using a famous game of Kayle. Find the complexity and implementation of Sprague Grundy theorem and game of kayle.

game theory

Nimber Arithmetic : A deeper dive in Nim

Explore Nimber Arithmetic in Game theory and always win a game. Nimbers have two particular operations. nim-addition and nim-multiplication. the nimbers are know as Grundy Numbers. Explore applications in the Game of Nim and odd Knight of the round table problem.

game theory

Exploring The Game of Nim

Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. The key to the theory of the game is the binary digital sum of the heap sizes "exclusive or" (xor). It is called the nim-sum. Find implementations of winning strategy and applications

mathematical algorithm

Bell Numbers: Number of partitions of a set

Bell numbers are a sequence of numbers that describe the number of ways a set with N elements can be partitioned into disjoint, non-empty subsets. Dobinski's Formula Satifaction Sum of Sterling's number of second kind, The Peirce Triangle Method. First few Bell numbers are 1, 1, 2, 5, 15, 52, 203

catalan number

Catalan Numbers

Catalan Numbers are one of the widest used and evident number patterns. They are named after the Belgian mathematician Eugène Charles Catalan. A sequence of natural numbers that occur in various counting problems. The Catalan numbers are: 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786,

greatest common divisor

Euclidean Algorithm to Calculate Greatest Common Divisor (GCD) of 2 numbers

The Euclid's algorithm (or Euclidean Algorithm) is a method for efficiently finding the greatest common divisor (GCD) of two numbers. The GCD of two integers X and Y is the largest integer that divides both of X and Y (without leaving a remainder).

sieve theory

The Sieve of Eratosthenes

Sieve of Eratosthenes is a simple and ancient algorithm (over 2200 years old) used to find the prime numbers up to any given limit. It is one of the most efficient ways to find small prime numbers. Implementations in C, C++, C Sharp, Java, Go, Haskell, JavaScript, PHP and Python.