🧮 NumberTheory-Based-Algorithms

Welcome to Number Theory Based Algorithms — a comprehensive, hands-on collection of essential and advanced Number Theory algorithms implemented in both Java and Python.
This repository is designed for competitive programmers, math enthusiasts, and algorithmic learners who wish to deeply understand and efficiently implement number-theoretic techniques.

All algorithms here are explained in detail on my YouTube channel — where I teach every concept from scratch, with complete mathematical proofs, examples, and live coding.
🎥 Watch all tutorials here: Code with Bharadwaj

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📘 Repository Overview

This repository contains efficient, well-structured implementations of core number theory algorithms. Each file is named in order, covering a wide range of concepts — from prime sieving to cryptographic number operations.

#	Algorithm Name	Java File	Python File
88	Sieve of Eratosthenes	88.SieveOfEratosthenesAlgo.java	88.SieveOfEratosthenesAlgo.py
89	Segmented Sieve	89.SegmentedSieveAlgo.java	89.SegmentedSieveAlgo.py
90	Euclidean Algorithm (GCD)	90.EuclideanAlgo.java	90.EuclideanAlgo.py
91	Extended Euclidean Algorithm	91.ExtendedEuclideanAlgo.java	91.ExtendedEuclideanAlgo.py
92	Modular Exponentiation	92.ModularExponentiationAlgo.java	92.ModularExponentiationAlgo.py
93	Modular Inverse	93.ModularInverseAlgo.java	93.ModularInverseAlgo.py
94	Chinese Remainder Theorem	94.ChineseRemainderTheoremAlgo.java	94.ChineseRemainderTheoremAlgo.py
95	Euler’s Totient Function	95.Euler’sTotientFunctionAlgo.java	95.Euler’sTotientFunctionAlgo.py
96	Miller–Rabin Primality Test	96.Miller–RabinPrimalityTestAlgo.java	96.Miller–RabinPrimalityTestAlgo.py
97	Pollard’s Rho Factorization	97.Pollard’sRhoFactorizationAlgo.java	97.Pollard’sRhoFactorizationAlgo.py
98	Fast Fourier Transform (FFT)	98.FastFourierTransformAlgo.java	98.FastFourierTransformAlgo.py
99	Number Theoretic Transform (NTT)	99.NumberTheoreticTransformAlgo.java	99.NumberTheoreticTransformAlgo.py

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🧠 What You’ll Learn

Each algorithm comes with:

• ✅ Clean, optimized code for Java and Python
• 🧩 Mathematical explanations behind the logic
• ⚡ Time and space complexity analysis
• 💡 Real-world and competitive programming applications

Topics covered include:

• Prime number generation and testing
• Modular arithmetic and exponentiation
• GCD, LCM, and modular inverses
• Chinese Remainder Theorem
• Euler’s Totient and number-theoretic transforms
• Cryptographic factorization and primality algorithms

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🎓 Learn with My YouTube Tutorials

I’ve personally explained and demonstrated all these algorithms on my YouTube channel, with visuals, dry runs, and mathematical proofs for each one.
📺 Watch them here → Code with Bharadwaj

Perfect for mastering Number Theory in Competitive Programming and understanding the math behind algorithms like RSA, FFT, and modular systems.

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🧰 Tech Stack

• Languages: Java & Python
• Java I/O: BufferedReader, PrintWriter for fast input/output
• Design: Focused on clarity, modularity, and algorithmic performance
• IDE: IntelliJ IDEA / VS Code

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👨‍💻 Author

Manu Bharadwaj BN
🎥 YouTube: Code with Bharadwaj
💻 GitHub: Manu577228
🌐 Portfolio

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🌟 Support & Contribute

If you find this repository useful:

• ⭐ Star this repository
• 🔔 Subscribe on YouTube
• 🧠 Fork and contribute your implementations

“Mathematics is the language in which God has written the universe.” — Galileo Galilei

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📄 License

Released under the MIT License — feel free to use, modify, and share with proper credit.