diff --git a/Maths/MobiusFunction.js b/Maths/MobiusFunction.js new file mode 100644 index 000000000..cde05792e --- /dev/null +++ b/Maths/MobiusFunction.js @@ -0,0 +1,29 @@ +/* + * Author: Akshay Dubey (https://github.com/itsAkshayDubey) + * Mobius Function: https://en.wikipedia.org/wiki/M%C3%B6bius_function + * For any positive integer n, define μ(n) as the sum of the primitive nth roots of unity. + * It has values in {−1, 0, 1} depending on the factorization of n into prime factors: + * μ(n) = +1 if n is a square-free positive integer with an even number of prime factors. + * μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors. + * μ(n) = 0 if n has a squared prime factor. + */ + +/** + * @function mobiusFunction + * @description -> This method returns μ(n) of given number n + * returns 1 when number is less than or equals 1 + * or number has even number of prime factors + * returns 0 when number has repeated prime factor + * returns -1 when number has odd number of prime factors + * @param {Integer} number + * @returns {Integer} + */ + +import { PrimeFactors } from './PrimeFactors.js' +export const mobiusFunction = (number) => { + const primeFactorsArray = PrimeFactors(number) + if (number <= 0) { + throw new Error('Number must be greater than zero.') + } + return primeFactorsArray.length !== new Set(primeFactorsArray).size ? 0 : primeFactorsArray.length % 2 === 0 ? 1 : -1 +} diff --git a/Maths/test/MobiusFunction.test.js b/Maths/test/MobiusFunction.test.js new file mode 100644 index 000000000..78b87261c --- /dev/null +++ b/Maths/test/MobiusFunction.test.js @@ -0,0 +1,19 @@ +import { mobiusFunction } from '../MobiusFunction' + +const expectedValuesArray = [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0, 1, 1, 1, 0, -1, 0, 0, 0] + +describe('Testing mobius function', () => { + for (let i = 1; i <= 100; i++) { + it('Testing for number = ' + i + ', should return ' + expectedValuesArray[i], () => { + expect(mobiusFunction(i)).toBe(expectedValuesArray[i - 1]) + }) + } + + it('should throw error when supplied negative numbers', () => { + expect(() => { mobiusFunction(-1) }).toThrow(Error) + }) + + it('should throw error when supplied zero', () => { + expect(() => { mobiusFunction(0) }).toThrow(Error) + }) +})