Algorithms that run our Universe

Goldbach's Conjecture

In this article, we shall be looking at the intriguing Goldbach's Conjecture, one of the best known unsolved problems in mathematics. Later on, in the article, we shall find the Goldbach pairs of all numbers that range from 1000 to 2000.

Algorithms

Average height of Random Binary Tree

In this article, we have explored an insightful approach/ algorithm to find the average height of Random Binary Tree which is of the order O(N^0.5). This will strengthen our understanding of binary trees and their applications.

Algorithms

Average height of nodes in a Binary Tree

In this article, we have explored an insightful approach/ algorithm to find the average height of nodes in the given Binary Tree. This will strengthen our understanding of binary trees and their applications.

Algorithms

Fermat’s Last Theorem

In this article, we will be talking about Fermat's Last Theorem , also called as Fermat's Great theorem. Stated by Pierre de Fermat in around 1637 in a margin of his copy of Arithmetica. A Nightmare for Mathematicians to prove.

Algorithms

Closest Pair of Points

In this article, we have explored different algorithms using which we can find the Closest Pair of Points in a given set of N points efficiently in O(N logN) time. This involves the idea of Divide and Conquer.

Time Complexity

Time & Space Complexity of AVL Tree operations

In this article, we will dive into the Time & Space Complexity and Complexity analysis of various AVL Tree operations like searching, inserting and deleting for different cases like Worst, Best and Average Case.

Time Complexity

Time & Space Complexity of Binary Tree operations

In this article, we will be discussing Time and Space Complexity of most commonly used binary tree operations like insert, search and delete for worst, best and average case.

Algorithms

Number of Integral points inside a rectangle

In this article, we have explored an insightful approach/ algorithm to find the number of interior integral points of a rectangle. This is an important concept in the field of computational geometry.

Algorithms

Voronoi Diagram

In this article, we discuss the voronoi diagram in depth and how to use Fortunes Sweep Line algorithm to compute it. This is an important topic in Computational Geometry.

Algorithms

Oriented area of a triangle

In this article, we discuss how to find the area of an oriented Polygon using the shoelace algorithm and as an example we find the area of an oriented triangle.

Algorithms

Self Crossing Problem

This article delves into the illustrious Self Crossing problem and looks at how we can solve it. This can be solved efficiently using Computational Geometry ideas.

Algorithms

Select a random node from Linked list

In this article, we have presented two algorithms to select a random node from Linked list efficiently while maintaining uniform randomness.

Algorithms

Swap two bits in a number

In this problem, we have to swap bits in a given number or an integer. This can be solved in constant time O(1) using XOR operation.

Algorithms

Union of Two Arrays

In this article, we have explained different approaches to find Union of Two Arrays and provided implementations in C++, Java and Python.

Algorithms

Check if given point is inside a convex polygon

In this post, we discuss how to check if a given point is inside a convex polygon using the Graham scan algorithm and list application areas for the solution.

Algorithms

Pick’s Theorem in Computational Geometry

In this post, we discuss Pick's theorem, its proof and example use cases where its application would be efficient to solve a problem. Using Pick's Theorem, we can compute the area of simple polygons.

Algorithms

Consistent Hashing

Consistent Hashing is a distributed hashing scheme that operates independently of the number of servers in a distributed hash table.

Algorithms

Number of Integral points inside a triangle

In this article, we have explored an insightful approach/ algorithm to find the number of interior integral points of a triangle. This is an important concept in the field of computational geometry.

List of Mathematical Algorithms

Pollard’s rho algorithm for factorization

Pollard's Rho Algorithm is a very interesting and quite accessible algorithm for factoring numbers. It was invented by John Pollard in 1975. It is not the fastest algorithm by far but in practice it outperforms trial division.

Algorithms

List of Randomized Algorithms

In this article, we have listed several important Randomized Algorithms such as Fisher Yates shuffle, Minimum Cut with Karger's, Matrix Product Verification and many more.

Algorithms

Find mirror image of point in 2D plane

In this article, we will learn how to find the mirror image position of a point in a 2D plane along with C++ implementation of the approach.

Algorithms

3 Sum Smaller Problem

The 3 sum smaller problem is an interesting algorithm problem that we shall be solving in this article. This is an extension of the 3 Sum Problem. In this, we have to select 3 different elements from an array such that the sum is less than a target.

Algorithms

Sum and Number of Divisors of a Number

In this post, we discuss formulas for getting the number of divisors of a number and their sum, additionally we will implement an algorithm that solves this problem.

Time Complexity

Time and Space Complexity of Interpolation Search

In this post, we discuss interpolation search algorithm, its best, average and worst case time complexity and compare it with its counterpart search algorithms. We derive the average case Time Complexity of O(loglogN) as well.

computational geometry

Number of integral points between two points

In this post, we solve an algebraic geometrical problem using programming whereby we find the number of integral points between two given two points.