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Algorithms

Algorithms have proven to be the most important domain over the last century which has reformed the way we do tasks. It is actively used to design industry systems and forms the building blocks of companies like Google. We cover all types of algorithms in depth

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.

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.

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.

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.

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.

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.

Delete middle element of Stack

In this article, we discuss an iterative and recursive approach to delete the middle element of a stack.

Nearest smaller and greater numbers with same number of set bits

In this article, we shall explore the various ways we can find the Nearest smaller and greater numbers with same number of set bits for given number.

computational geometry

Find mirror image of point in 3D plane

In this article, we will learn how to find the mirror image of a point (x,y,z) in 3D-plane.

Longest Substring with at Least K repeating characters

In this article, we have presented two algorithms to find the Longest Substring with at Least K repeating characters.

Find smallest of 3 integers without comparison

In this guide, we will go through how to get the smallest of three numbers without using Comparison operation. We have presented 3 different techniques using decrement, division and shift operation.

Legendre's conjecture

In this article, we have explained Legendre's conjecture, presented an implementation of an Algorithm to verify Legendre's conjecture till a given limit and have provided output which you can analyze.

Shortest distance between a Line and Point in 3D plane

In this article, we have presented two algorithms to find the Shortest distance between a Line and Point in 3D plane. This involves idea of Projection and Parallelogram.

Absolute value of Integer using Bitwise Operations

In this article, we have explained two approaches to find the Absolute value of Integer using Bitwise Operations namely Right shift, OR and XOR operations.

Furthest Pair of Points (+ Rotating Calipers Method)

In this article, we have explained how to solve the problem of Furthest Pair of Points using Rotating Calipers Method. We have presented the naive approach as well.

Parallel Bubble Sort

In this article, we have explored how to implement Bubble Sort in parallel on multiple threads / cores. We have presented two approaches: one is slower than the sequential approach but the other approach is significantly faster than all other approaches for large input.

Average Height of Random Binary Search Tree

In this post, we discuss the average height of a Random Binary Search Tree (BST) (that is 4.31107 ln(N) - 1.9531 lnln(N) + O(1)) by discussing various lemmas and their proofs. We omit full proofs and discuss the essential key points for easier understanding.

Time Complexity

Time and Space Complexity of Hash Table operations

This article covers Time and Space Complexity of Hash Table (also known as Hash Map) operations for different operations like search, insert and delete for two variants of Hash Table that is Open and Closed Addressing.

Delaunay Triangulation

In this article, we discuss Delaunay Triangulation, its relation to Voronoi diagrams and algorithms to compute Delaunay Triangulation. This is an important topic in Computational Geometry.

Create a Heap from Array of N integers

In this post, we discuss the heap data structure and how to create a min and max heap from N given integers in form of an Array. Similarly, inserting elements one by one take O(N logN) time but the optimal approach takes O(N) time.