diff --git a/Maths/ModularArithmetic.js b/Maths/ModularArithmetic.js new file mode 100644 index 0000000000..26c54ebbb4 --- /dev/null +++ b/Maths/ModularArithmetic.js @@ -0,0 +1,56 @@ +import { extendedEuclideanGCD } from './ExtendedEuclideanGCD' + +/** + * https://brilliant.org/wiki/modular-arithmetic/ + * @param {Number} arg1 first argument + * @param {Number} arg2 second argument + * @returns {Number} + */ + +export class ModRing { + constructor (MOD) { + this.MOD = MOD + } + + isInputValid = (arg1, arg2) => { + if (!this.MOD) { + throw new Error('Modulus must be initialized in the object constructor') + } + if (typeof arg1 !== 'number' || typeof arg2 !== 'number') { + throw new TypeError('Input must be Numbers') + } + } + /** + * Modulus is Distributive property, + * As a result, we separate it into numbers in order to keep it within MOD's range + */ + + add = (arg1, arg2) => { + this.isInputValid(arg1, arg2) + return ((arg1 % this.MOD) + (arg2 % this.MOD)) % this.MOD + } + + subtract = (arg1, arg2) => { + this.isInputValid(arg1, arg2) + // An extra MOD is added to check negative results + return ((arg1 % this.MOD) - (arg2 % this.MOD) + this.MOD) % this.MOD + } + + multiply = (arg1, arg2) => { + this.isInputValid(arg1, arg2) + return ((arg1 % this.MOD) * (arg2 % this.MOD)) % this.MOD + } + + /** + * + * It is not Possible to find Division directly like the above methods, + * So we have to use the Extended Euclidean Theorem for finding Multiplicative Inverse + * https://github.com/TheAlgorithms/JavaScript/blob/master/Maths/ExtendedEuclideanGCD.js + */ + + divide = (arg1, arg2) => { + // 1st Index contains the required result + // The theorem may have return Negative value, we need to add MOD to make it Positive + return (extendedEuclideanGCD(arg1, arg2)[1] + this.MOD) % this.MOD + } +} diff --git a/Maths/test/ModularArithmetic.test.js b/Maths/test/ModularArithmetic.test.js new file mode 100644 index 0000000000..af42e243de --- /dev/null +++ b/Maths/test/ModularArithmetic.test.js @@ -0,0 +1,45 @@ +import { ModRing } from '../ModularArithmetic' + +describe('Modular Arithmetic', () => { + const MOD = 10000007 + let ring + beforeEach(() => { + ring = new ModRing(MOD) + }) + + describe('add', () => { + it('Should return 9999993 for 10000000 and 10000000', () => { + expect(ring.add(10000000, 10000000)).toBe(9999993) + }) + it('Should return 9999986 for 10000000 and 20000000', () => { + expect(ring.add(10000000, 20000000)).toBe(9999986) + }) + }) + + describe('subtract', () => { + it('Should return 1000000 for 10000000 and 9000000', () => { + expect(ring.subtract(10000000, 9000000)).toBe(1000000) + }) + it('Should return 7 for 10000000 and 20000000', () => { + expect(ring.subtract(10000000, 20000000)).toBe(7) + }) + }) + + describe('multiply', () => { + it('Should return 1000000 for 100000 and 10000', () => { + expect(ring.multiply(100000, 10000)).toBe(9999307) + }) + it('Should return 7 for 100000 and 10000100', () => { + expect(ring.multiply(10000000, 20000000)).toBe(98) + }) + }) + + describe('divide', () => { + it('Should return 4 for 3 and 11', () => { + expect(ring.divide(3, 11)).toBe(4) + }) + it('Should return 2 for 18 and 7', () => { + expect(ring.divide(18, 7)).toBe(2) + }) + }) +}) pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy