algorithm: mobius function implementation (#1088)

* feat: Add mobius function implementation

* test: Add tests for mobius function

* fix: Code style fixes

* fix: Code style fixes

* fix: Store prime factors in a variable &  add throw error

* fix: Fix unit tests for zero and negative numbers

* fix: Minor code style fixes
This commit is contained in:
Akshay Dubey
2022-09-06 15:25:28 +05:30
committed by GitHub
parent ad41e8cc1c
commit 6f55ed4a1f
2 changed files with 48 additions and 0 deletions

29
Maths/MobiusFunction.js Normal file
View File

@ -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
}