# Zig Math Algorithms

A collection of mathematical algorithms implemented in Zig, designed for educational purposes and showcasing Zig's performance.

## 🚀 Table of Contents

- [Zig Math Algorithms](#zig-math-algorithms)
  - [🚀 Table of Contents](#-table-of-contents)
  - [🔢 Available Algorithms](#-available-algorithms)
  - [🚀 Prerequisites](#-prerequisites)
  - [🔧 Running the Algorithms](#-running-the-algorithms)
  - [📚 Purpose](#-purpose)
  - [🤝 Contributing](#-contributing)
  - [📧 Contact](#-contact)

## 🔢 Available Algorithms


| Algorithm | Description | Command | Difficulty |
|-----------|-------------|---------|------------|
| **Basic Number Operations** |
| Armstrong Number Checker | Verifies Armstrong numbers | `zig run src/algorithm/math/is_armstrong.zig` | Easy |
| Digital Root | Recursive digit sum calculation | `zig run src/algorithm/math/digital_root.zig` | Easy |
| Happy Number Checker | Checks if a number is happy | `zig run src/algorithm/math/happy_number.zig` | Easy |
| Integer Square Root | Finds floor(√n) | `zig run src/algorithm/math/integer_sqrt.zig` | Easy |
| Leap Year Checker | Determines if year is leap | `zig run src/algorithm/math/leap_year_checker.zig` | Easy |
| Palindrome Number Checker | Checks if a number is a palindrome | `zig run src/algorithm/math/palindrome_number.zig` | Easy |
| Power of Two Checker | Checks if number is 2ⁿ | `zig run src/algorithm/math/power_of_two.zig` | Easy |
| Prime Number Checker | Checks if a number is prime | `zig run src/algorithm/math/prime_checker.zig` | Easy |
| Reverse Number | Reverses digits of a number | `zig run src/algorithm/math/reverse_number.zig` | Easy |
| Sum of Digits | Calculates digit sum | `zig run src/algorithm/math/sum_of_digits.zig` | Easy |
| **Number Theory** |
| Abundant/Deficient Checker | Checks if number is abundant/deficient | `zig run src/algorithm/math/abundant_deficient_checker.zig` | Easy |
| Perfect Number Checker | Checks if a number is perfect | `zig run src/algorithm/math/perfect_number_checker.zig` | Easy |
| Strong Number Checker | Sum of digit factorials check | `zig run src/algorithm/math/strong_number_checker.zig` | Easy |
| GCD and LCM Calculator | Finds GCD and LCM | `zig run src/algorithm/math/gcd_lcm_calculator.zig` | Medium |
| Prime Counter | Counts primes up to n | `zig run src/algorithm/math/prime_counter.zig` | Medium |
| Prime Factorization | Computes prime factors | `zig run src/algorithm/math/prime_factorization.zig` | Medium |
| Euler's Totient Function | Counts coprime numbers | `zig run src/algorithm/math/euler_totient.zig` | Hard |
| **Sequences and Series** |
| Factorial Calculator | Calculates n! | `zig run src/algorithm/math/factorial.zig` | Easy |
| Fibonacci Calculator | Calculates nth Fibonacci | `zig run src/algorithm/math/fibonacci.zig` | Easy |
| Lucas Numbers | Generates Lucas numbers | `zig run src/algorithm/math/lucas_numbers.zig` | Easy |
| Sequence Generator | Arithmetic/Geometric sequences | `zig run src/algorithm/math/sequence_generator.zig` | Easy |
| Collatz Conjecture | Steps to reach 1 | `zig run src/algorithm/math/collatz_conjecture.zig` | Medium |
| Trailing Zeros in Factorial | Counts trailing zeros in n! | `zig run src/algorithm/math/factorial_trailing_zeroes.zig` | Medium |
| Catalan Calculator | Calculates nth Catalan | `zig run src/algorithm/math/catalan.zig` | Hard |
| **Advanced Mathematics** |
| Binomial Coefficient | Pascal's triangle coefficients | `zig run src/algorithm/math/binomial_coefficient.zig` | Medium |
| Matrix Multiplication | Performs matrix multiplication | `zig run src/algorithm/math/matrix_multiplication.zig` | Medium |
| Monte Carlo Pi | Estimates π using Monte Carlo simulation | `zig run src/algorithm/math/monte_carlo_pi.zig` | Medium |
| Quadratic Solver | Solves quadratic equations (ax² + bx + c = 0) | `zig run src/algorithm/math/quadratic_solver.zig` | Medium |
| Cantor Set Generator | Generates Cantor set | `zig run src/algorithm/math/cantor_set.zig -- 0 1 3` | Hard |
| Chinese Remainder | Solves linear congruences | `zig run src/algorithm/math/chinese_remainder.zig` | Hard |
| Extended Euclidean | GCD and Bézout coefficients | `zig run src/algorithm/math/euclidean_algorithm_extended.zig` | Hard |
| Linear Interpolation | Linear interpolation | `zig run src/algorithm/math/linear_interpolation.zig` | Hard |
| Cartesian to Polar | Converts cartesian to polar coordinates | `zig run src/algorithm/math/cartesian_to_polar.zig` | Medium |
| Fast Fibonacci | Optimized Fibonacci calculation | `zig run src/algorithm/math/fibonacci_fast.zig` | Medium |
| Fibonacci Dynamic Programming | DP approach for Fibonacci | `zig run src/algorithm/math/fibonacci_dynamic_programming.zig` | Medium |
| Fibonacci Binet Formula | Binet's formula for Fibonacci | `zig run src/algorithm/math/fibonacci_bnet_formula.zig` | Medium |
| Fermat's Factorization | Integer factorization method | `zig run src/algorithm/math/fermats_factorization.zig` | Hard |
| Fast Fourier Transform | FFT implementation | `zig run src/algorithm/math/fft.zig` | Hard |
| Greatest Common Divisor | Alternative GCD implementation | `zig run src/algorithm/math/greatest_common_divisor.zig` | Medium |
| Karatsuba Multiplication | Fast multiplication algorithm | `zig run src/algorithm/math/karatsuba.zig` | Hard |
| Knapsack Problem | Dynamic programming solution | `zig run src/algorithm/math/knapsack.zig` | Hard |
| Large Factorials | Big number factorial calculation | `zig run src/algorithm/math/large_factorials.zig` | Hard |
| Modular Exponentiation | Fast modular exponentiation | `zig run src/algorithm/math/modular_exponentiation.zig` | Medium |
| Newton-Raphson Method | Root-finding algorithm | `zig run src/algorithm/math/newton_raphson.zig` | Hard |
| Pascal's Triangle | Generate Pascal's triangle | `zig run src/algorithm/math/pascals_triangle.zig` | Medium |
| Polynomial Addition | Add two polynomials | `zig run src/algorithm/math/polynomial_add.zig` | Medium |
| Series Sum | Calculate sum of series | `zig run src/algorithm/math/series_sum.zig` | Easy |
| Sieve of Eratosthenes | Prime number generation | `zig run src/algorithm/math/sieve_of_eratosthenes.zig` | Medium |

## 🚀 Prerequisites

- **Zig Compiler**: 
  - Latest version recommended. Install via:

    ```shell
    sh -c "$(curl -fsSL https://ziglang.org/download/index.json | jq -r '.master.url')"
    ```

## 🔧 Running the Algorithms

To run any algorithm, use the Zig run command followed by the specific algorithm file path and any required arguments. For example:

```shell
zig run src/algorithm/math/prime_checker.zig
# or
zig test src/algorithm/math/prime_checker.zig
```

More information is available in the respective file comment header.

## 📚 Purpose

This repository provides a collection of mathematical algorithms implemented in Zig, showcasing the language's capabilities and performance. Each module is designed to be easily run and tested, making it a useful resource for learning and experimentation.

## 🤝 Contributing
Contributions are welcome! Here's how to contribute:
- Fork the repository
- Create your feature branch (git checkout -b feature/AmazingFeature)
- Commit your changes (git commit -m 'Add some AmazingFeature')
- Push to the branch (git push origin feature/AmazingFeature)
- Open a pull request

## 📧 Contact

Ramsyana - ramsyana[at]mac[dot]com

I'm a system engineering enthusiast. Feel free to fork, clone, open issues, or contribute to this project. Don’t hesitate to reach out with any questions, suggestions, or collaboration ideas!