README.md

Algorithms

Here is a custom implementation of many algorithms. Edits and improvements are welcomed. Below is a list for a quick transition.

Sorting algorithms

• Exchange Sorts
  • Bubble sort
  • Cocktail shaker sort or bidirectional bubble sort
  • Comb sort
  • Quicksort♻️
    • Iterative
    • Recursion
  • Odd–even sort♻️
  • Gnome sort
• Hybrid
  • Timsort♻️
• Insertion sorts
  • Insertion sort
    • Binary insertion sort
  • Shell sort
  • Tree sort♻️
• Merge sorts
  • Merge sort♻️
• Selection sorts
  • Heapsort♻️
  • Selection sort
• Distribution sorts
  • Counting sort
  • Radix sort♻️

Numerical algorithms

• Root finding♻️  
  • Bisection method
  • Newton's method
    • Simplified Newton's method
  • Secant method
  • Сhords method
  • Сombined method
  • Iterative method
    • Fixed-point iteration method
• Solving systems of linear equations
  • Gauss–Seidel method
  • Gaussian elimination
• Interpolation and extrapolation🌀
  • Spline interpolation
  • Bilinear interpolation
  • Inverse interpolation
  • Interpolation with a Newton polynomial
• Calculation of integrals
  • Left rectangles method
  • Right rectangles method
  • Middle rectangles method
  • Simpson method
  • 3/8 method
  • Trapezium method
  • Gauss's method 🌀
• Differentiation🌀

Cryptography

(presented in this repository)

• Asymmetric (public key) encryption
  • DSA
  • RSA
  • ElGamal
• Cryptographic hash functions
  • HMAC
  • MD5
  • SHA-2
• Cryptographically secure pseudo-random number generators
  • Fortuna
  • Yarrow algorithm
• Key exchange
  • Diffie–Hellman key exchange
• Key derivation function
• Symmetric (secret key) encryption
  • Advanced Encryption Standard (AES)
  • Data Encryption Standard (DES)

Computer graphics

• Picture Modifications(rotate, zoom, transfer)🌀
• Line Drawing
  • Bresenham's line algorithm
    • Without smoothing
      • With integers
      • With floats/doubles
    • With smoothing
  • DDA line algorithm♻️
• Circle and Ellips Drawing🌀
  • According to the equation
    • Сanonical equation
    • Parametric equation
  • Bresenham's algorithm
  • Midpoint circle/ellips algorithm
• Filling Algorithms🌀
  • The algorithm with the sorted list of edges
  • The algorithm in the ribs
  • The algorithm with partition
  • The algorithm with the flag
• Clipping
  • Cohen–Sutherland
  • Half-division algorithm
  • Simple algorithm

Number theoretic algorithms

• Multiplication algorithms
  • Karatsuba algorithm
  • Schönhage–Strassen algorithm
  • Fürer’s algorithm
• Algorithms of modular arithmetic
  • Montgomery modular multiplication
  • Algorithm for finding the order of an element
• Exponentiation by squaring
• Discrete logarithm
  • Baby-step giant-step
• Algorithms for finding the greatest common divisor (GCD) of two numbers
  • Euclid's algorithm
  • Extended Euclidean algorithm
  • Binary GCD algorithm
• Prime number
  • Finding prime numbers
    • Trial division
    • Sieve of Eratosthenes
    • Sieve of Atkin
  • Primality tests
    • Deterministic tests of primality
      • Fermat primality test
      • AKS primality test
      • Lucas primality test
    • Probabilistic tests of primality
      • Miller–Rabin primality test
• Integer factorization
  • Algorithms with exponential complexity
    • Trial division
    • Fermat's factorization method
  • Algorithms with subexponential complexity
    • Quadratic sieve
    • ...
• Multiplying matrices
  • Strassen algorithm

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Structures

Primitive types

• Boolean
• Character
• Floating-point
• Double
• Integer
• String
• Reference (also called a pointer or handle)
• Enumerated type

Materials used

• Article in Russian and in English
• Wiki: List of algorithms and List of data structures
• AlgoList (in Russian)

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COMMENT:

This list can use links to other my projects where these algorithms were used. There may be errors and shortcomings. These algorithms will be divided into separate modules and improved in the last turn due to lack of time.

Legend:

• ✅ - ОК
• ⚠️ - problem
• 🆘 - need help
• ♻️ - need update
• 🌀 - in process