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Merged
merged 7 commits into from
Sep 6, 2022
Merged

algorithm: mobius function implementation #1088

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01785bf
feat: Add mobius function implementation
itsAkshayDubey Sep 3, 2022
376edfe
test: Add tests for mobius function
itsAkshayDubey Sep 3, 2022
47ded10
fix: Code style fixes
itsAkshayDubey Sep 3, 2022
f3ec996
fix: Code style fixes
itsAkshayDubey Sep 3, 2022
148ef6c
fix: Store prime factors in a variable & add throw error
itsAkshayDubey Sep 6, 2022
2affaa1
fix: Fix unit tests for zero and negative numbers
itsAkshayDubey Sep 6, 2022
844bc2a
fix: Minor code style fixes
itsAkshayDubey Sep 6, 2022
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29 changes: 29 additions & 0 deletions Maths/MobiusFunction.js
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/*
* 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
}
19 changes: 19 additions & 0 deletions Maths/test/MobiusFunction.test.js
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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)
})
})