List of Mathematical Algorithms

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

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).

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

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.

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.

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

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.

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.

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.

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.

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

Gale Shapley Algorithm is an efficient algorithm that is used to solve the Stable Matching problem. It takes O(N^2) time complexity where N is the number of people involved.

We are given an array, we need to find the minimum number of increment and decrement operations (by 1) required to make all the array elements equal. We have explored two approaches where brute force approach take O(N^2) time while the efficient approach O(N logN) time.

We are given a sorted array which might have duplicate elements, our task is to find the minimum number of increment (by 1) operations needed to make the elements of an array unique. We have solved this using two approaches one using two pointers and other using hashmap.

In this article, we have explored different applications of Catalan Numbers such as number of valid parenthesis expressions, number of rooted binary trees with n internal nodes, number of ways are there to cut an (n+2)-gon into n triangles and many more.

We are given two numbers M and N. Our aim is to find the highest power of N that divides Factorial of M (M!). First we have discussed about the Brute Force approach and then we will be discussing this problem using Legendre’s formula.

Kadane's Algorithm is commonly known for Finding the largest sum of a subarray in linear time O(N). We have presented 3 variants of Kadane's Algorithm along with in-depth explanation of basic ideas.

Binary GCD algorithm or Stein's algorithm is an algorithm that calculates two non-negative integer's largest common divisor by using simpler arithmetic operations than the standard euclidean algorithm and it reinstates division by numerical shifts, comparisons, and subtraction operations.

We are given an array and we need to find the minimum number of operations required to make GCD of the array equal to k. Where an operation could be either increment or decrement an array element by 1. We have solved this in O(N log N) time complexity.

Given an array of size N . Find the number of increment (by 1) operations required to make the array in increasing order. In each move, we can add 1 to any element in the array.