algorithm: mobius function implementation (TheAlgorithms#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

Author: itsAkshayDubey

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'
+exportconstmobiusFunction=(number)=>{
+constprimeFactorsArray=PrimeFactors(number)
+if(number<=0){
+thrownewError('Number must be greater than zero.')
+}
+returnprimeFactorsArray.length!==newSet(primeFactorsArray).size ? 0 : primeFactorsArray.length%2===0 ? 1 : -1
+}

Maths/test/MobiusFunction.test.js

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+import{mobiusFunction}from'../MobiusFunction'
+
+constexpectedValuesArray=[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(leti=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)
+})
+})