[rational-numbers] Add new practice exercise

Author: IsaacG

config.json

@@ -1551,6 +1551,14 @@
           "logic"
         ]
       },
+      {
+        "slug": "rational-numbers",
+        "name": "Rational Numbers",
+        "uuid": "c129f1a1-851b-4261-8da3-44224cc5564d",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
+      },
       {
         "slug": "resistor-color-trio",
         "name": "Resistor Color Trio",

exercises/practice/rational-numbers/.docs/instructions.md

@@ -0,0 +1,42 @@
+# Instructions
+
+A rational number is defined as the quotient of two integers `a` and `b`, called the numerator and denominator, respectively, where `b != 0`.
+
+~~~~exercism/note
+Note that mathematically, the denominator can't be zero.
+However in many implementations of rational numbers, you will find that the denominator is allowed to be zero with behaviour similar to positive or negative infinity in floating point numbers.
+In those cases, the denominator and numerator generally still can't both be zero at once.
+~~~~
+
+The absolute value `|r|` of the rational number `r = a/b` is equal to `|a|/|b|`.
+
+The sum of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ + r₂ = a₁/b₁ + a₂/b₂ = (a₁ * b₂ + a₂ * b₁) / (b₁ * b₂)`.
+
+The difference of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ - r₂ = a₁/b₁ - a₂/b₂ = (a₁ * b₂ - a₂ * b₁) / (b₁ * b₂)`.
+
+The product (multiplication) of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ * r₂ = (a₁ * a₂) / (b₁ * b₂)`.
+
+Dividing a rational number `r₁ = a₁/b₁` by another `r₂ = a₂/b₂` is `r₁ / r₂ = (a₁ * b₂) / (a₂ * b₁)` if `a₂` is not zero.
+
+Exponentiation of a rational number `r = a/b` to a non-negative integer power `n` is `r^n = (a^n)/(b^n)`.
+
+Exponentiation of a rational number `r = a/b` to a negative integer power `n` is `r^n = (b^m)/(a^m)`, where `m = |n|`.
+
+Exponentiation of a rational number `r = a/b` to a real (floating-point) number `x` is the quotient `(a^x)/(b^x)`, which is a real number.
+
+Exponentiation of a real number `x` to a rational number `r = a/b` is `x^(a/b) = root(x^a, b)`, where `root(p, q)` is the `q`th root of `p`.
+
+Implement the following operations:
+
+- addition, subtraction, multiplication and division of two rational numbers,
+- absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.
+
+Your implementation of rational numbers should always be reduced to lowest terms.
+For example, `4/4` should reduce to `1/1`, `30/60` should reduce to `1/2`, `12/8` should reduce to `3/2`, etc.
+To reduce a rational number `r = a/b`, divide `a` and `b` by the greatest common divisor (gcd) of `a` and `b`.
+So, for example, `gcd(12, 8) = 4`, so `r = 12/8` can be reduced to `(12/4)/(8/4) = 3/2`.
+The reduced form of a rational number should be in "standard form" (the denominator should always be a positive integer).
+If a denominator with a negative integer is present, multiply both numerator and denominator by `-1` to ensure standard form is reached.
+For example, `3/-4` should be reduced to `-3/4`
+
+Assume that the programming language you are using does not have an implementation of rational numbers.

exercises/practice/rational-numbers/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "IsaacG"
+  ],
+  "files": {
+    "solution": [
+      "rational_numbers.go"
+    ],
+    "test": [
+      "rational_numbers_test.go"
+    ],
+    "example": [
+      ".meta/example.go"
+    ]
+  },
+  "blurb": "Implement rational numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Rational_number"
+}

exercises/practice/rational-numbers/.meta/example.go

@@ -0,0 +1,70 @@
+package rationalnumbers
+
+import "math"
+
+func abs(a int) int {
+	if a < 0 {
+		return -a
+	}
+	return a
+}
+
+func pow(a, b int) int {
+	return int(math.Pow(float64(a), float64(b)))
+}
+
+// gcd calculates the Greatest Common Divisor of two integers using the Euclidean algorithm.
+func gcd(a, b int) int {
+	for b != 0 {
+		a, b = b, a%b // This swaps a and b and updates b with the remainder
+	}
+	return a
+}
+
+type Rational struct {
+	numerator, denominator int
+}
+
+func Reduce(r Rational) Rational {
+	gcd := abs(gcd(r.numerator, r.denominator))
+	if r.denominator < 0 {
+		gcd *= -1
+	}
+	return Rational{r.numerator / gcd, r.denominator / gcd}
+}
+
+func Add(a, b Rational) Rational {
+	numerator := a.numerator*b.denominator + b.numerator*a.denominator
+	denominator := a.denominator * b.denominator
+	return Reduce(Rational{numerator, denominator})
+}
+
+func Sub(a, b Rational) Rational {
+	numerator := a.numerator*b.denominator - b.numerator*a.denominator
+	denominator := a.denominator * b.denominator
+	return Reduce(Rational{numerator, denominator})
+}
+
+func Mul(a, b Rational) Rational {
+	return Reduce(Rational{a.numerator * b.numerator, a.denominator * b.denominator})
+}
+
+func Div(a, b Rational) Rational {
+	return Reduce(Rational{a.numerator * b.denominator, b.numerator * a.denominator})
+}
+
+func Abs(r Rational) Rational {
+	return Reduce(Rational{abs(r.numerator), abs(r.denominator)})
+}
+
+func Exprational(base Rational, power int) Rational {
+	if power >= 0 {
+		return Reduce(Rational{pow(base.numerator, power), pow(base.denominator, power)})
+	}
+	power = -power
+	return Reduce(Rational{pow(base.denominator, power), pow(base.numerator, power)})
+}
+
+func Expreal(base int, power Rational) float64 {
+	return math.Pow(math.Pow(float64(base), float64(power.numerator)), 1/float64(power.denominator))
+}

exercises/practice/rational-numbers/.meta/gen.go

@@ -0,0 +1,186 @@
+package main
+
+import (
+	"../../../../gen"
+	"fmt"
+	"log"
+	"text/template"
+)
+
+func main() {
+	t, err := template.New("").Parse(tmpl)
+	if err != nil {
+		log.Fatal(err)
+	}
+	j := map[string]any{
+		"abs": &[]testCaseUnaryRationalToRational{},
+		"add": &[]testCaseBinaryRationalToRational{},
+		"div": &[]testCaseBinaryRationalToRational{},
+		"mul": &[]testCaseBinaryRationalToRational{},
+		"sub": &[]testCaseBinaryRationalToRational{},
+		"exprational": &[]testCaseExprational{},
+		"expreal": &[]testCaseExpreal{},
+		"reduce": &[]testCaseUnaryRationalToRational{},
+	}
+	if err := gen.Gen("rational-numbers", j, t); err != nil {
+		log.Fatal(err)
+	}
+}
+
+type Rational [2]int
+
+func (r Rational) String() string {
+	return fmt.Sprintf("Rational{%d, %d}", r[0], r[1])
+}
+
+type RationalPair struct {
+	R1 Rational `json:"r1"`
+	R2 Rational `json:"r2"`
+}
+
+func (r RationalPair) String() string {
+	return fmt.Sprintf("[2]Rational{{%d, %d}, {%d, %d}}", r.R1[0], r.R1[1], r.R2[0], r.R2[1])
+}
+
+type testCaseUnaryRationalToRational struct {
+	Description string `json:"description"`
+	Input       struct {
+		R Rational `json:"r"`
+	} `json:"input"`
+	Expected    Rational `json:"expected"`
+}
+
+type testCaseBinaryRationalToRational struct {
+	Description string `json:"description"`
+	Input       RationalPair `json:"input"`
+	Expected    Rational `json:"expected"`
+}
+
+type testCaseExprational struct {
+	Description string `json:"description"`
+	Input       struct {
+		R Rational `json:"r"`
+		N int `json:"n"`
+	} `json:"input"`
+	Expected Rational `json:"expected"`
+}
+
+type testCaseExpreal struct {
+	Description string `json:"description"`
+	Input       struct {
+		X int `json:"x"`
+		R Rational `json:"r"`
+	} `json:"input"`
+	Expected float64 `json:"expected"`
+}
+
+var tmpl = `{{.Header}}
+
+var testCasesAbs = []struct {
+	description string
+	input       Rational
+	expected    Rational
+}{
+{{range .J.abs}}{
+	description: 	{{printf "%q" .Description}},
+	input:	        {{.Input.R}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesAdd = []struct {
+	description string
+	input       [2]Rational
+	expected    Rational
+}{
+{{range .J.add}}{
+	description: 	{{printf "%q" .Description}},
+	input:	        {{.Input}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesSub = []struct {
+	description string
+	input       [2]Rational
+	expected    Rational
+}{
+{{range .J.sub}}{
+	description: 	{{printf "%q" .Description}},
+	input:	        {{.Input}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesMul = []struct {
+	description string
+	input       [2]Rational
+	expected    Rational
+}{
+{{range .J.mul}}{
+	description: 	{{printf "%q" .Description}},
+	input:	        {{.Input}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesDiv = []struct {
+	description string
+	input       [2]Rational
+	expected    Rational
+}{
+{{range .J.div}}{
+	description: 	{{printf "%q" .Description}},
+	input:	        {{.Input}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesExprational = []struct {
+	description string
+	inputR      Rational
+	inputInt    int
+	expected    Rational
+}{
+{{range .J.exprational}}{
+	description: 	{{printf "%q" .Description}},
+	inputR:         {{.Input.R}},
+	inputInt:       {{.Input.N}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesExpreal = []struct {
+	description string
+	inputInt    int
+	inputR      Rational
+	expected    float64
+}{
+{{range .J.expreal}}{
+	description: 	{{printf "%q" .Description}},
+	inputInt:       {{.Input.X}},
+	inputR:         {{.Input.R}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+
+var testCasesReduce = []struct {
+	description string
+	input       Rational
+	expected    Rational
+}{
+{{range .J.reduce}}{
+	description: 	{{printf "%q" .Description}},
+	input:	        {{.Input.R}},
+	expected:    	{{.Expected}},
+},
+{{end}}
+}
+`