feat: Add mobius function (TheAlgorithms#532)

math/mobius.go

@@ -0,0 +1,38 @@
+// mobius.go
+// description: Returns μ(n)
+// details:
+// 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.
+// wikipedia: https://en.wikipedia.org/wiki/M%C3%B6bius_function
+// author: Akshay Dubey (https://github.com/itsAkshayDubey)
+// see mobius_test.go
+
+package math
+
+import (
+	"github.com/TheAlgorithms/Go/math/prime"
+)
+
+// Mu is the Mobius function
+// This function returns μ(n) for given number
+func Mu(n int) int {
+	if n <= 1 {
+		return 1
+	}
+	var primeFactorCount int
+	for i := 1; i <= n; i++ {
+		if n%i == 0 && prime.OptimizedTrialDivision(int64(i)) {
+			if n%(i*i) == 0 {
+				return 0
+			}
+			primeFactorCount += 1
+		}
+	}
+	if primeFactorCount%2 == 0 {
+		return 1
+	}
+	return -1
+}

math/mobius_test.go

@@ -0,0 +1,41 @@
+// mobius_test.go
+// description: Returns μ(n)
+// author: Akshay Dubey (https://github.com/itsAkshayDubey)
+// see mobius.go
+
+package math_test
+
+import (
+	"testing"
+
+	algmath "github.com/TheAlgorithms/Go/math"
+)
+
+func TestMu(t *testing.T) {
+	var tests = []struct {
+		n        int
+		expected int
+	}{
+		{-1, 1},
+		{0, 1},
+		{2, -1},
+		{3, -1},
+		{95, 1},
+		{97, -1},
+		{98, 0},
+		{99, 0},
+		{100, 0},
+	}
+	for _, test := range tests {
+		result := algmath.Mu(test.n)
+		t.Log(test.n, " ", result)
+		if result != test.expected {
+			t.Errorf("Wrong result! Expected:%v, returned:%v ", test.expected, result)
+		}
+	}
+}
+func BenchmarkMu(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		algmath.Mu(65536)
+	}
+}