Algorithms that run our Universe

Detect Cycle in Undirected Graph using Union Find algorithm

In this article, we've explored the approach to detect a cycle in undirected graph using union-find algorithm. This takes O(VE) Time Complexity.

Time Complexity

Amortized Time Complexity

In this article, we have explored the concept of Amortized Time Complexity by taking an example and compared it with a related concept: Average Case Time Complexity.

Culture

OpenGenus Visual Documentation

In this article, we give a detailed documentation of the development of OpenGenus Visual project which is an open-source Visualization tool for Algorithms and Data Structures.

computational geometry

Art Gallery Problem

In this article, we have explored Art Gallery Problem in depth along with variants of Art Gallery Problem and important results.

Algorithms

Data Structure for Spreadsheet / Excel

In this article, we have explored several Data Structures that are used in Spreadsheet / Excel Sheet. These involve ideas like Sparse Matrix, AVL Tree and much more.

Problems on Binary Tree

Select Random Node from Binary Tree

In this article, we have presented two algorithms to select a random node from Binary Tree while maintaining the uniform randomness.

List of Mathematical Algorithms

Firoozbakht’s conjecture

In this article, we have explored Firoozbakht’s conjecture in depth. Firoozbakht's conjecture is linked to upper limits for the prime gap function in terms of n. Asymptotic outcomes for both the conjecture and the function help us understand the interrelationships.

Algorithms

Cayley’s formula

In this article, we have explained the idea of Cayley’s formula which is used to find the number of trees with N nodes and M connected components. We have presented an implementation to calculate Cayley’s formula.

computational geometry

Check if 4 Line Segments form a Rectangle

In this article, we will solve the problem of Check if 4 Line Segments form a Rectangle. This is a core problem of Computational Geometry.

Time Complexity

Time and Space Complexity of Circular Linked List

In this article, we have explored Time and Space Complexity of Circular Linked List. We have covered different cases like Worst Case, Average Case and Best Case.

Time Complexity

Time and Space complexity of Binary Search Tree (BST)

In this article, we are going to explore and calculate about the time and space complexity of binary search tree operations.

Time Complexity

Time and Space Complexity of Red Black Tree

In this article, we will look at the Time and Space Complexity analysis of various Red-Black Tree operations including searching, inserting, and deleting for worst, best, and average cases.

Time Complexity

Time and Space Complexity of Stooge Sort

In this article, we will be discussing the time and space complexity of Stooge Sort covering various cases like Worst, Best and Average Case.

Data Structures

Array Data Structure

In this article, we have explored Array Data Structure in depth. We explore key ideas in Array and how we develop our own custom implementation of Array along with different Array operations.

Algorithms

Quick Sort with two pivots (Dual-Pivot)

Quick Sort is a Sorting Algorithm that takes a divide-and-conquer approach. We will be looking at how to do this while selecting two pivots points instead of one.

Time Complexity

Time and Space Complexity of Queue

This article is about the analysis of time and space complexity of queue operations. With this, we will also learn what the time and space complexity are and how we can calculate the time and space complexity of an algorithm.

Algorithms

Dutch National Flag Problem

In this article, we have explored the Dutch National Flag Problem which is a standard Algorithmic Problem proposed by Edsger Dijkstra. It is solved efficiently using Three Way Partitioning technique.

Algorithms

3 Way Partitioning Quick Sort

In this article, we have explored 3 Way Partitioning Quick Sort in depth. This is relatively faster than 2 way Quick Sort (Normal version) in practical applications.

Algorithms

Three Way Partitioning

In this article, we have explored Three Way Partitioning technique which is used in Three Partition Quicksort and Dutch National Flag Algorithm.

computational geometry

Euler’s Polyhedron Formula

In this article, we have explored Euler’s Polyhedron Formula in depth with examples, proof and applications in real life problems.

Time Complexity

Time and Space Complexity of Stack

In this article, we will explore about various operations on Stack Data Structure and the Time and Space Complexity of each operation for various cases like Best case, Average case and Worst case.

Algorithms

Josephus Problem

In this article, we have explored and solved Josephus Problem in depth which is a Standard Problem in Computer Science. We have presented two solutions to Josephus Problem.

Time Complexity

Time and Space complexity of Trie

In this article, we will understand the Complexity analysis of various Trie operations. We have covered Time and Space Complexity of Trie for various cases like Best case, Average Case and Worst Case.

Time Complexity

Time and Space Complexity of Heap data structure operations

In this article, we have explored the Time and Space Complexity of Heap data structure operations including different cases like Worst, Average and Best case. At the end, we have added a table summarizes the complexities.

Algorithms

Delete middle element of Queue

In this article, we discuss how to delete the middle element of a queue without using other data structures. We have explained both iterative and recursive approach.