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Mathematical Algorithms

Last Updated : 01 Dec, 2024
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The following is the list of mathematical coding problem ordered topic wise. Please refer Mathematical Algorithms (Difficulty Wise) for the difficulty wise list of problems.

GCD and LCM:

  • GCD of Two Numbers
  • LCM of Two Numbers
  • LCM of array
  • GCD of array
  • Basic and Extended Euclidean
  • Stein’s Algorithm for GCD
  • GCD, LCM and Distributive Property
  • Count pairs with gcd (A, B) as B
  • GCD of floating point numbers
  • Series with largest GCD and sum equals to n
  • Largest Subset with GCD 1
  • Summation of GCD of all the pairs up to N

Divisibility & Large Numbers:

  • Divisibility by 3
  • Divisibility by 4
  • Divisibility by 6
  • Divisibility by 7
  • Divisibility by 9
  • Divisibility by 11
  • Divisibility by 12
  • Divisibility by 13
  • Divisibility by 15
  • Divisibility by 29

Series:

  • Juggler Sequence
  • Padovan Sequence
  • Aliquot Sequence
  • Moser-de Bruijn Sequence
  • Stern-Brocot Sequence
  • Newman-Conway Sequence
  • Sylvester’s sequence
  • Recaman’s sequence
  • Sum of 2, 22, 222, ………
  • Sum of 1^2 + 3^2 + 5^2 + . . . + (2*n – 1)^2
  • Sum of 0.6, 0.06, 0.006, 0.0006, …to n terms
  • n-th term of 2, 12, 36, 80, 150….

Number Digits:

  • Minimum digits to remove to make a number Perfect Square
  • Print first k digits of 1/n where n is a positive integer
  • Check if a given number can be represented in given a no. of digits in any base
  • Find element using minimum segments in Seven Segment Display
  • Find next greater number with same set of digits
  • Check if a number is jumbled or not
  • Numbers having difference with digit sum more than s
  • Total numbers with no repeated digits in a range
  • K-th digit in ‘a’ raised to power ‘b’

Algebra:

  • Program to add two polynomials
  • Multiply two polynomials
  • Find number of solutions of a linear equation of n variables
  • Calculate the Discriminant Value
  • Program for dot product and cross product of two vectors
  • Iterated Logarithm log*(n)
  • Program to find correlation coefficient
  • Program for Muller Method
  • Number of non-negative integral solutions of a + b + c = n
  • Generate Pythagorean Triplets

Number System:

  • Exponential notation of a decimal number
  • Check if a number is power of k using base changing method
  • Convert a binary number to hexadecimal number
  • Program for decimal to hexadecimal conversion
  • Converting a Real Number (between 0 and 1) to Binary String
  • Convert from any base to decimal and vice versa
  • Decimal to binary conversion without using arithmetic operators

Prime Numbers & Primality Tests:

  • Prime Numbers
  • Left-Truncatable Prime
  • Mersenne Prime
  • Super Prime
  • Hardy-Ramanujan Theorem
  • Rosser’s Theorem
  • Fermat’s little theorem
  • Introduction to Primality Test and School Method
  • Vantieghems Theorem for Primality Test
  • AKS Primality Test
  • Lucas Primality Test

Prime Factorization & Divisors:

  • Prime factors
  • Smith Numbers
  • Sphenic Number
  • Hoax Number
  • k-th prime factor of a given number
  • Pollard’s Rho Algorithm for Prime Factorization
  • Finding power of prime number p in n!
  • Find all divisors of a natural number
  • Find numbers with n-divisors in a given range

Modular Arithmetic:

  • Modular Exponentiation (Power in Modular Arithmetic)
  • Modular multiplicative inverse
  • Modular Division
  • Euler’s criterion (Check if square root under modulo p exists)
  • Find sum of modulo K of first N natural number
  • How to compute mod of a big number?
  • Exponential Squaring (Fast Modulo Multiplication)
  • Trick for modular division ( (x1 * x2 …. xn) / b ) mod (m)

Factorial:

  • Program for factorial of a number
  • Legendre’s formula (Given p and n, find the largest x such that p^x divides n!)
  • Count trailing zeroes in factorial of a number
  • Factorial of a large number
  • Primorial of a number
  • Find maximum power of a number that divides a factorial
  • Largest power of k in n! (factorial) where k may not be prime
  • Check if a number is a Krishnamurthy Number or not
  • Last non-zero digit of a factorial
  • Count digits in a factorial using Logarithm

Fibonacci Numbers:

  • Fibonacci Numbers
  • Interesting facts about Fibonacci numbers
  • Zeckendorf’s Theorem (Non-Neighbouring Fibonacci Representation)
  • Finding nth Fibonacci Number using Golden Ratio
  • Matrix Exponentiation
  • Fibonacci Coding
  • Cassini’s Identity
  • Tail Recursion for Fibonacci

Catalan Numbers:

  • Catalan numbers
  • Applications of Catalan Numbers
  • Dyck path
  • Succinct Encoding of Binary Tree
  • Find the number of valid parentheses expressions of given length

nCr Computations:

  • Binomial Coefficient
  • Introduction and Dynamic Programming solution to compute nCr%p
  • Program to calculate value of nCr
  • Rencontres Number (Counting partial derangements)
  • Sum of squares of binomial coefficients
  • Space and time efficient Binomial Coefficient
  • Horner’s Method for Polynomial Evaluation

Set Theory:

  • Power Set
  • Minimize the absolute difference of sum of two subsets
  • Sum of all subsets of a set formed by first n natural numbers
  • Sum of average of all subsets
  • Bell Numbers (Number of ways to Partition a Set)

Sieve Algorithms:

  • Sieve of Eratosthenes
  • Segmented Sieve
  • Sieve of Atkin
  • Sieve of Sundaram to print all primes smaller than n
  • Sieve of Eratosthenes in 0(n) time complexity
  • Prime Factorization using Sieve O(log n) for multiple queries

Euler Totient Function:

  • Euler’s Totient Function
  • Optimized Euler Totient Function for Multiple Evaluations
  • Euler’s Totient function for all numbers smaller than or equal to n
  • Primitive root of a prime number n modulo n
  • Euler’s Four Square Identity

Chinese Remainder Theorem:

  • Introduction to Chinese Remainder Theorem
  • Implementation of Chinese Remainder theorem (Inverse Modulo based implementation)
  • Cyclic Redundancy Check and Modulo-2 Division
  • Using Chinese Remainder Theorem to Combine Modular equations

Some Practice Problems:

  • Interquartile Range (IQR)
  • Simulated Annealing
  • Pseudo Random Number Generator (PRNG)
  • Square root of a number using log
  • Find ways an Integer can be expressed as sum of n-th power of unique natural numbers
  • N-th root of a number
  • Fast Fourier Transformation for poynomial multiplication
  • Find Harmonic mean using Arithmetic mean and Geometric mean
  • Double Base Palindrome
  • Program for Derivative of a Polynomial
  • Sgn value of a polynomial
  • Check if a number is a power of another number
  • Program to evaluate simple expressions
  • Make a fair coin from a biased coin
  • Implement *, – and / operations using only + arithmetic operator

Quick Links :

  • Learn Data Structure and Algorithms | DSA Tutorial
  • Practrice Problems on Mathematical Algorithms
  • Quizzes on Mathematical Algorithms
  • Videos on Mathematical Algorithms

Next Article
Geometric Algorithms

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