feat: Add egyptian fractions example.

README.md

@@ -11,6 +11,7 @@ So far, the following exercises have been covered:
 - [Clever max](./clevermax/) – calculates the maximum of two numbers
 - [Cons, Car, Cdr & co.](./cons) – implements a cons cell and the corresponding functions
 - [Continous maximum](./continuousmax/) – calculates the maximum of a sliding window
+- [Egyptian fractions](./egyptianfractions/) – calculates the "Egyptian Fractions" version of a given fraction
 - [Floyd](./floyd/) – implements Floyd's cycle-finding "Tortoise and Hare" algorithm
 - [Heap](./heap/) – implements a heap from scratch, without using the built-in `container/heap` package
 - [Markov count](./markovcount/) – figures out how often states are reached by a Markov chain

egyptianfractions/documentation.go

@@ -0,0 +1,2 @@
+// Package egyptianfractions calculates the "Egyptian Fractions" version of a given fraction
+package egyptianfractions

egyptianfractions/extend.go

@@ -0,0 +1,16 @@
+package egyptianfractions
+
+func Extend(a, b Fraction) (Fraction, Fraction) {
+	denominator := a.Denominator * b.Denominator
+
+	extendedA := Fraction{
+		Numerator:   a.Numerator * b.Denominator,
+		Denominator: denominator,
+	}
+	extendedB := Fraction{
+		Numerator:   b.Numerator * a.Denominator,
+		Denominator: denominator,
+	}
+
+	return extendedA, extendedB
+}

egyptianfractions/extend_test.go

@@ -0,0 +1,22 @@
+package egyptianfractions_test
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/thenativeweb/codingcircle/egyptianfractions"
+)
+
+func TestExtend(t *testing.T) {
+	fractionA := egyptianfractions.Fraction{1, 3}
+	fractionB := egyptianfractions.Fraction{4, 7}
+
+	extendedFractionA, extendedFractionB :=
+		egyptianfractions.Extend(fractionA, fractionB)
+
+	assert.Equal(t, 7, extendedFractionA.Numerator)
+	assert.Equal(t, 21, extendedFractionA.Denominator)
+
+	assert.Equal(t, 12, extendedFractionB.Numerator)
+	assert.Equal(t, 21, extendedFractionB.Denominator)
+}

egyptianfractions/find_egyptian_fractions.go

@@ -0,0 +1,27 @@
+package egyptianfractions
+
+import "math"
+
+func FindEgyptianFractions(fraction Fraction) []Fraction {
+	fractions := []Fraction{}
+
+	for fraction.Numerator > 0 {
+		n := int(math.Ceil(
+			float64(fraction.Denominator) /
+				float64(fraction.Numerator)))
+
+		partialFraction := Fraction{1, n}
+
+		fractions = append(fractions, partialFraction)
+
+		extendedFraction, extendedPartialFraction :=
+			Extend(fraction, partialFraction)
+
+		fraction = Reduce(Fraction{
+			Numerator:   extendedFraction.Numerator - extendedPartialFraction.Numerator,
+			Denominator: extendedFraction.Denominator,
+		})
+	}
+
+	return fractions
+}

egyptianfractions/find_egyptian_fractions_test.go

@@ -0,0 +1,34 @@
+package egyptianfractions_test
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/thenativeweb/codingcircle/egyptianfractions"
+)
+
+func TestFindEgyptianFractions(t *testing.T) {
+	t.Run("returns 1/2 and 1/6 for 2/3", func(t *testing.T) {
+		fraction := egyptianfractions.Fraction{2, 3}
+
+		result := egyptianfractions.FindEgyptianFractions(fraction)
+
+		assert.Equal(
+			t,
+			[]egyptianfractions.Fraction{{1, 2}, {1, 6}},
+			result,
+		)
+	})
+
+	t.Run("returns 1/3, 1/11 and 1/231 for 3/7", func(t *testing.T) {
+		fraction := egyptianfractions.Fraction{3, 7}
+
+		result := egyptianfractions.FindEgyptianFractions(fraction)
+
+		assert.Equal(
+			t,
+			[]egyptianfractions.Fraction{{1, 3}, {1, 11}, {1, 231}},
+			result,
+		)
+	})
+}

egyptianfractions/fraction.go

@@ -0,0 +1,6 @@
+package egyptianfractions
+
+type Fraction struct {
+	Numerator   int
+	Denominator int
+}

egyptianfractions/gcd.go

@@ -0,0 +1,10 @@
+package egyptianfractions
+
+func GCD(a, b int) int {
+	for b != 0 {
+		remainder := a % b
+		a = b
+		b = remainder
+	}
+	return a
+}

egyptianfractions/gcd_test.go

@@ -0,0 +1,20 @@
+package egyptianfractions_test
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/thenativeweb/codingcircle/egyptianfractions"
+)
+
+func TestGCD(t *testing.T) {
+	t.Run("returns the greatest common divisor if one exists", func(t *testing.T) {
+		result := egyptianfractions.GCD(8, 12)
+		assert.Equal(t, 4, result)
+	})
+
+	t.Run("returns 1 if no greatest common divisor exists", func(t *testing.T) {
+		result := egyptianfractions.GCD(2, 3)
+		assert.Equal(t, 1, result)
+	})
+}

egyptianfractions/reduce.go

@@ -0,0 +1,10 @@
+package egyptianfractions
+
+func Reduce(fraction Fraction) Fraction {
+	divisor := GCD(fraction.Numerator, fraction.Denominator)
+
+	return Fraction{
+		Numerator:   fraction.Numerator / divisor,
+		Denominator: fraction.Denominator / divisor,
+	}
+}

egyptianfractions/reduce_test.go

@@ -0,0 +1,20 @@
+package egyptianfractions_test
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/thenativeweb/codingcircle/egyptianfractions"
+)
+
+func TestReduce(t *testing.T) {
+	fraction := egyptianfractions.Fraction{
+		Numerator:   4,
+		Denominator: 8,
+	}
+
+	reducedFraction := egyptianfractions.Reduce(fraction)
+
+	assert.Equal(t, 1, reducedFraction.Numerator)
+	assert.Equal(t, 2, reducedFraction.Denominator)
+}