Mathematical Algorithms
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Practice Problems on Mathematical Algorithms
Topics:
- Check if a large number is divisible by 3 or not
- Check if a large number is divisible by 4 or not
- Check if a large number is divisible by 6 or not
- Check divisibility by 7
- Check if a large number is divisible by 9 or not
- Check if a large number is divisible by 11 or not
- Divisibility by 12 for a large number
- Check if a large number is divisible by 13 or not
- Check if a large number is divisibility by 15
- Number is divisible by 29 or not
- LCM of array
- GCD of array
- Basic and Extended Euclidean algorithms
- Stein’s Algorithm for finding GCD
- GCD, LCM and Distributive Property
- Count number of pairs (A <= N, B <= N) such that gcd (A, B) is B
- Program to find 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
- Juggler Sequence
- Padovan Sequence
- Aliquot Sequence
- Moser-de Bruijn Sequence
- Stern-Brocot Sequence
- Newman-Conway Sequence
- Sylvester’s sequence
- Recaman’s sequence
- Sum of the sequence 2, 22, 222, ………
- Sum of series 1^2 + 3^2 + 5^2 + . . . + (2*n – 1)^2
- Sum of the series 0.6, 0.06, 0.006, 0.0006, …to n terms
- n-th term in series 2, 12, 36, 80, 150….
- 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’
- 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
- 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 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)
- 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
- 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
- Applications of Catalan Numbers
- Dyck path
- Succinct Encoding of Binary Tree
- Find the number of valid parentheses expressions of given length
- 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
- 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 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’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
- 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
- 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
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