List of Mathematical Algorithms

Adding 2 integers as linked lists

We will represent an Integer as Singly Linked List and define an addition algorithm to add two integers as Linked Lists. This is used to add very large integers which is not stored in existing data types.

Algorithms

Swap 2 variables [6+ techniques]

We have explored about Swapping of 2 variables. We have presented different methods to do so including swapping using third variable, using arithmetic operations, XOR, macro and much more along with their pros and cons.

Algorithms

Lempel Ziv Welch compression and decompression

In this article, we will learn about the Lempel Ziv Welch compression and decompression algorithm, a famous compression technique that is widely used in Unix systems and GIF format files

Algorithms

Lomuto Partition Scheme

We have explained the Lomuto partition scheme, which is used in the famous Quicksort algorithm. It is an algorithm to partition an array into two parts based on a given condition.

Algorithms

Shuffle an array [2 approaches]

We have explored two approaches to shuffle an array. The first approach uses an auxiliary array while the second approach is in-place and is known as Fisher Yates Algorithm.

Algorithms

Boyer Moore majority vote algorithm [Majority Element]

Boyer Moore voting algorithm is used to find the majority element among the given sequence of elements which occurs more than N/2 times, in linear time complexity and constant space complexity.

Algorithms

Number of rectangles from a given set of points

We have discussed how to find the number of rectangles (parallel to the axes) possible from a given set of coordinate points.

Algorithms

Factorial of large numbers

Factorial of a non-negative number n, denoted by n!, is the product of all positive numbers less than or equal to n. With the usual approach, we can compute factorial only till 20! due to size limitation of data type. We have present how to overcome this limitation.

Algorithms

Move negative elements to front of array

This article focuses on the algorithm to move the negative elements of an array to the front. This can be solved by the two-pointer approach.

Algorithms

Find GCD of all elements in an array

In this article, we have presented an algorithm to find the Greatest Common Divisor (GCD) of all elements of an array efficiently.

List of Mathematical Algorithms

Find index such that sum of left sub-array = right sub-array (Equilibrium Index)

For a given array, we need to find an index such that sum of left sub-array = right sub-array also called the Equilibrium Index. We solve this using brute force approach O(N^2) and using prefix array in linear O(N) time.

Algorithms

Finding LCM of an array of numbers

Find the LCM of the given array of positive numbers. We have explored 2 approaches: one using GCD and other without using GCD.

Algorithms

Maximum XOR of two numbers in an array using Trie

Given a list of numbers we need to identify a pair of numbers in the list such that the XOR of those numbers is the maximum possible over all the pairs.

Algorithms

Munchausen Number

A number that is equal to the sum of its digits each raised to the power equal to its digit is a Munchausen Number or perfect digit-to-digit invariant(PDDI).

Algorithms

Counting derangements

Given any integer N, we need to find out the number of Derangements for a set of N elements.

Algorithms

What is a Disarium Number?

A disarium number is a number in which the sum of the digits to the power of their respective position is equal to the number itself (position is counted from left to right starting from 1).

Algorithms

Minimum steps to make binary string empty by removing alternating subsequence in each step

Given a string str consisting of only '0's and '1's, the task is to make the string empty by performing minimum number of operations. An operation is defined as the removal of an alternating subsequence from str without changing the order of the remaining characters.

Algorithms

Minimum elements to be removed from array to make the sum even

Given an array of integer and you have to find minimum no of integers or elements from array need to be removed so that sum of all elements of array results an even value.

Algorithms

Find number of solutions of a linear equation of N variables

We have to find the number of solutions to a linear equation of N variables. We have solved this using Dynamic Programming.

Algorithms

Algorithms for Calculating Day of Week

Some of the Algorithms for Calculating Day of Week are: Tomohiko Sakamoto Algorithm, Gausses Algorithm and Wang's Algorithm. We have covered the basics of Julian and Georgian calender as well.

Software Engineering

SHA1 Algorithm (+ JavaScript Implementation)

In this article, we have explained the algorithmic steps in SHA1 Algorithm in depth. We have demonstrated an example by implementing SHA1 algorithm in JavaScript.

Algorithms

Minimum number of increment operations to make K elements of an array equal

Given an array arr[] of n elements and an integer k, the task is to make any k elements of the array equal by performing only increment operations. This is solved using sliding window technique.

Algorithms

Tomohiko Sakamoto Algorithm

Tomohiko Sakamoto Algorithm is used to find the Day of the week for a given date. The date is provided according to the Gregorian Calendar.

Algorithms

Minimum number of operations to make XOR of array equal to zero

You are given an array of n non-negative integers. Your task is to find the minimum number of operations to make XOR of array equal to zero.

Algorithms

Carmichael Number

Carmichael Number is an odd composite number which follows the following condition applicable in Fermat's Little Theorem.