competitive-math-toolkit v1.0.4

Competitive Math Toolkit 🚀

A high-performance math library optimized for competitive programming.

📌 Features

✔️ Number Theory: GCD, LCM, Modular Exponentiation, Modular Inverse, Prime Sieve, Chinese Remainder Theorem
✔️ Combinatorics: Factorial, nCr (Combinations), Catalan Numbers
✔️ Matrix Exponentiation: Fast Fibonacci, Solving Recurrence Relations
✔️ Graph Math: Eulerian Path Detection
✔️ Optimized for O(log n) and O(1) operations wherever possible

📦 Installation

npm install competitive-math-toolkit

🔰 Usage

1️⃣ Number Theory

const mathToolkit = require("competitive-math-toolkit");

console.log(mathToolkit.gcd(36, 60)); // Output: 12
console.log(mathToolkit.lcm(12, 15)); // Output: 60
console.log(mathToolkit.modExp(2, 10, 1000000007)); // Output: 1024
console.log(mathToolkit.sieve(50)); // Output: [2, 3, 5, 7, 11, 13, ...]
console.log(mathToolkit.isDivisible(10, 5)); // Output: "Yes"
console.log(mathToolkit.findDivisors(10)); // Output: [1, 2, 5, 10]
console.log(mathToolkit.primeFactorization(60)); // Output: [2, 2, 3, 5]
console.log(mathToolkit.isPrime(13)); // Output: true
console.log(mathToolkit.modAdd(10, 15, 7)); // Output: 4
console.log(mathToolkit.modSubtract(10, 15, 7)); // Output: 2
console.log(mathToolkit.modMultiply(10, 15, 7)); // Output: 1
console.log(mathToolkit.modInverse(3, 11)); // Output: 4
console.log(mathToolkit.modDivide(10, 5, 7)); // Output: 2
console.log(mathToolkit.nthRoot(3, 27)); // Output: 3
console.log(mathToolkit.isPerfectSquare(25)); // Output: true
console.log(mathToolkit.isPerfectCube(27)); // Output: true
console.log(mathToolkit.binaryExponentiation(2, 10, 1000000007)); // Output: 1024
console.log(mathToolkit.isCoprime(14, 25)); // Output: true
console.log(mathToolkit.sumOfDivisors(12)); // Output: 28
console.log(mathToolkit.countPrimes(50)); // Output: 15

2️⃣ Combinatorics

console.log(mathToolkit.factorial(5)); // Output: 120
console.log(mathToolkit.nCr(5, 2)); // Output: 10
console.log(mathToolkit.nPr(5, 2)); // Output: 20

3️⃣ Matrix Exponentiation

console.log(mathToolkit.nthFibonacci(10)); // Output: 55

4️⃣ Graph Math

const graph = {
  A: ["B", "C"],
  B: ["A", "D"],
  C: ["A", "D"],
  D: ["B", "C"],
};
console.log(mathToolkit.countEulerianPaths(graph)); // Output: true

5️⃣ Chinese Remainder Theorem

const num = [3, 5, 7];
const rem = [2, 3, 2];

console.log(mathToolkit.chineseRemainderTheorem(num, rem)); // Output: 23

6️⃣ Bitwise Operations

Efficient bitwise operations and conversions.

const mathToolkit = require("competitive-math-toolkit");

console.log(mathToolkit.and(5, 3)); // Output: 1
console.log(mathToolkit.or(5, 3)); // Output: 7
console.log(mathToolkit.xor(5, 3)); // Output: 6
console.log(mathToolkit.not(5)); // Output: -6
console.log(mathToolkit.leftShift(5, 1)); // Output: 10
console.log(mathToolkit.rightShift(5, 1)); // Output: 2

console.log(mathToolkit.countSetBits(9)); // Output: 2
console.log(mathToolkit.isPowerOfTwo(8)); // Output: true

// Bitwise Manipulation
console.log(mathToolkit.setBit(5, 1)); // Output: 7
console.log(mathToolkit.clearBit(7, 1)); // Output: 5
console.log(mathToolkit.toggleBit(5, 0)); // Output: 4
console.log(mathToolkit.checkBit(5, 2)); // Output: true

// Conversions
console.log(mathToolkit.decimalToBinary(10)); // Output: "1010"
console.log(mathToolkit.binaryToDecimal("1010")); // Output: 10
console.log(mathToolkit.decimalToHex(255)); // Output: "FF"
console.log(mathToolkit.hexToDecimal("FF")); // Output: 255
console.log(mathToolkit.decimalToOctal(64)); // Output: "100"
console.log(mathToolkit.octalToDecimal("100")); // Output: 64
console.log(mathToolkit.binaryToHex("1111")); // Output: "F"
console.log(mathToolkit.hexToBinary("F")); // Output: "1111"

📜 API Reference

⚡ Performance

• Most operations are O(log N) for efficiency.
• Matrix exponentiation speeds up Fibonacci and recurrence relations.
• Uses modular arithmetic for safe computation.

🛠️ Running Tests

You can run unit tests using:

npm test

📝 License

This project is licensed under the MIT License.

🌟 Contributing

Feel free to contribute, report issues, or request new features!

1. Fork the repository.
2. Create a new branch: git checkout -b feature-new-feature
3. Commit changes: git commit -m "Added a new feature"
4. Push and submit a PR!

🚀 Future Enhancements

• ✅ Add big integer support
• ✅ Implement fast polynomial calculations
• ✅ Provide TypeScript support

👨‍💻 Author

Developed by Apurva Kumar 🚀
GitHub | LinkedIn