[#724] New practice exercise rational-numbers (#755)

Author: jiegillet

config.json

@@ -2398,6 +2398,22 @@
           "cond"
         ],
         "difficulty": 9
+      },
+      {
+        "slug": "rational-numbers",
+        "name": "Rational Numbers",
+        "uuid": "e2777a03-d890-453e-af5b-d61f60adbbf5",
+        "prerequisites": [
+          "pattern-matching",
+          "basics",
+          "integers",
+          "floating-point-numbers",
+          "guards"
+        ],
+        "practices": [
+          "basics"
+        ],
+        "difficulty": 4
       }
     ],
     "foregone": [

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

@@ -0,0 +1,30 @@
+# Description
+
+A rational number is defined as the quotient of two integers `a` and `b`, called the numerator and denominator, respectively, where `b != 0`.
+
+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`.
+
+Assume that the programming language you are using does not have an implementation of rational numbers.
+

exercises/practice/rational-numbers/.formatter.exs

@@ -0,0 +1,4 @@
+# Used by "mix format"
+[
+  inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
+]

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

@@ -0,0 +1,22 @@
+{
+  "blurb": "Implement rational numbers.",
+  "authors": [
+    "jiegillet"
+  ],
+  "contributors": [
+    "angelikatyborska"
+  ],
+  "files": {
+    "solution": [
+      "lib/rational_numbers.ex"
+    ],
+    "test": [
+      "test/rational_numbers_test.exs"
+    ],
+    "example": [
+      ".meta/example.ex"
+    ]
+  },
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Rational_number"
+}

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

@@ -0,0 +1,59 @@
+defmodule RationalNumbers do
+  @type rational :: {integer, integer}
+
+  @doc """
+  Add two rational numbers
+  """
+  @spec add(a :: rational, b :: rational) :: rational
+  def add({a, b}, {c, d}), do: {a * d + c * b, b * d} |> reduce
+
+  @doc """
+  Subtract two rational numbers
+  """
+  @spec subtract(a :: rational, b :: rational) :: rational
+  def subtract(a, {x, y}), do: add(a, {-x, y})
+
+  @doc """
+  Multiply two rational numbers
+  """
+  @spec multiply(a :: rational, b :: rational) :: rational
+  def multiply({a, b}, {c, d}), do: {a * c, b * d} |> reduce
+
+  @doc """
+  Divide two rational numbers
+  """
+  @spec divide_by(num :: rational, den :: rational) :: rational
+  def divide_by(num, {a, b}), do: multiply(num, {b, a})
+
+  @doc """
+  Absolute value of a rational number
+  """
+  @spec abs(a :: rational) :: rational
+  def abs({a, b}), do: {Kernel.abs(a), Kernel.abs(b)} |> reduce
+
+  @doc """
+  Exponentiation of a rational number by an integer
+  """
+  @spec pow_rational(a :: rational, n :: integer) :: rational
+  def pow_rational({a, b}, n) when n < 0, do: pow_rational({b, a}, -n)
+
+  def pow_rational({a, b}, n),
+    do: {:math.pow(a, n) |> round, :math.pow(b, n) |> round} |> reduce
+
+  @doc """
+  Exponentiation of a real number by a rational number
+  """
+  @spec pow_real(x :: float, n :: rational) :: float
+  def pow_real(x, {a, b}), do: :math.pow(x, a / b)
+
+  @doc """
+  Reduce a rational number to its lowest terms
+  """
+  @spec reduce(a :: rational) :: rational
+  def reduce({a, b}) when b < 0, do: reduce({-a, -b})
+
+  def reduce({a, b}) do
+    gcd = Integer.gcd(a, b)
+    {div(a, gcd), div(b, gcd)}
+  end
+end

exercises/practice/rational-numbers/.meta/tests.toml

@@ -0,0 +1,117 @@
+# This is an auto-generated file. Regular comments will be removed when this
+# file is regenerated. Regenerating will not touch any manually added keys,
+# so comments can be added in a "comment" key.
+
+[0ba4d988-044c-4ed5-9215-4d0bb8d0ae9f]
+description = "Add two positive rational numbers"
+
+[88ebc342-a2ac-4812-a656-7b664f718b6a]
+description = "Add a positive rational number and a negative rational number"
+
+[92ed09c2-991e-4082-a602-13557080205c]
+description = "Add two negative rational numbers"
+
+[6e58999e-3350-45fb-a104-aac7f4a9dd11]
+description = "Add a rational number to its additive inverse"
+
+[47bba350-9db1-4ab9-b412-4a7e1f72a66e]
+description = "Subtract two positive rational numbers"
+
+[93926e2a-3e82-4aee-98a7-fc33fb328e87]
+description = "Subtract a positive rational number and a negative rational number"
+
+[a965ba45-9b26-442b-bdc7-7728e4b8d4cc]
+description = "Subtract two negative rational numbers"
+
+[0df0e003-f68e-4209-8c6e-6a4e76af5058]
+description = "Subtract a rational number from itself"
+
+[34fde77a-75f4-4204-8050-8d3a937958d3]
+description = "Multiply two positive rational numbers"
+
+[6d015cf0-0ea3-41f1-93de-0b8e38e88bae]
+description = "Multiply a negative rational number by a positive rational number"
+
+[d1bf1b55-954e-41b1-8c92-9fc6beeb76fa]
+description = "Multiply two negative rational numbers"
+
+[a9b8f529-9ec7-4c79-a517-19365d779040]
+description = "Multiply a rational number by its reciprocal"
+
+[d89d6429-22fa-4368-ab04-9e01a44d3b48]
+description = "Multiply a rational number by 1"
+
+[0d95c8b9-1482-4ed7-bac9-b8694fa90145]
+description = "Multiply a rational number by 0"
+
+[1de088f4-64be-4e6e-93fd-5997ae7c9798]
+description = "Divide two positive rational numbers"
+
+[7d7983db-652a-4e66-981a-e921fb38d9a9]
+description = "Divide a positive rational number by a negative rational number"
+
+[1b434d1b-5b38-4cee-aaf5-b9495c399e34]
+description = "Divide two negative rational numbers"
+
+[d81c2ebf-3612-45a6-b4e0-f0d47812bd59]
+description = "Divide a rational number by 1"
+
+[5fee0d8e-5955-4324-acbe-54cdca94ddaa]
+description = "Absolute value of a positive rational number"
+
+[3cb570b6-c36a-4963-a380-c0834321bcaa]
+description = "Absolute value of a positive rational number with negative numerator and denominator"
+
+[6a05f9a0-1f6b-470b-8ff7-41af81773f25]
+description = "Absolute value of a negative rational number"
+
+[5d0f2336-3694-464f-8df9-f5852fda99dd]
+description = "Absolute value of a negative rational number with negative denominator"
+
+[f8e1ed4b-9dca-47fb-a01e-5311457b3118]
+description = "Absolute value of zero"
+
+[ea2ad2af-3dab-41e7-bb9f-bd6819668a84]
+description = "Raise a positive rational number to a positive integer power"
+
+[8168edd2-0af3-45b1-b03f-72c01332e10a]
+description = "Raise a negative rational number to a positive integer power"
+
+[e2f25b1d-e4de-4102-abc3-c2bb7c4591e4]
+description = "Raise zero to an integer power"
+
+[431cac50-ab8b-4d58-8e73-319d5404b762]
+description = "Raise one to an integer power"
+
+[7d164739-d68a-4a9c-b99f-dd77ce5d55e6]
+description = "Raise a positive rational number to the power of zero"
+
+[eb6bd5f5-f880-4bcd-8103-e736cb6e41d1]
+description = "Raise a negative rational number to the power of zero"
+
+[30b467dd-c158-46f5-9ffb-c106de2fd6fa]
+description = "Raise a real number to a positive rational number"
+
+[6e026bcc-be40-4b7b-ae22-eeaafc5a1789]
+description = "Raise a real number to a negative rational number"
+
+[9f866da7-e893-407f-8cd2-ee85d496eec5]
+description = "Raise a real number to a zero rational number"
+
+[0a63fbde-b59c-4c26-8237-1e0c73354d0a]
+description = "Reduce a positive rational number to lowest terms"
+
+[f87c2a4e-d29c-496e-a193-318c503e4402]
+description = "Reduce a negative rational number to lowest terms"
+
+[3b92ffc0-5b70-4a43-8885-8acee79cdaaf]
+description = "Reduce a rational number with a negative denominator to lowest terms"
+
+[c9dbd2e6-5ac0-4a41-84c1-48b645b4f663]
+description = "Reduce zero to lowest terms"
+
+[297b45ad-2054-4874-84d4-0358dc1b8887]
+description = "Reduce an integer to lowest terms"
+
+[a73a17fe-fe8c-4a1c-a63b-e7579e333d9e]
+description = "Reduce one to lowest terms"

exercises/practice/rational-numbers/lib/rational_numbers.ex

@@ -0,0 +1,59 @@
+defmodule RationalNumbers do
+  @type rational :: {integer, integer}
+
+  @doc """
+  Add two rational numbers
+  """
+  @spec add(a :: rational, b :: rational) :: rational
+  def add(a, b) do
+  end
+
+  @doc """
+  Subtract two rational numbers
+  """
+  @spec subtract(a :: rational, b :: rational) :: rational
+  def subtract(a, b) do
+  end
+
+  @doc """
+  Multiply two rational numbers
+  """
+  @spec multiply(a :: rational, b :: rational) :: rational
+  def multiply(a, b) do
+  end
+
+  @doc """
+  Divide two rational numbers
+  """
+  @spec divide_by(num :: rational, den :: rational) :: rational
+  def divide_by(num, den) do
+  end
+
+  @doc """
+  Absolute value of a rational number
+  """
+  @spec abs(a :: rational) :: rational
+  def abs(a) do
+  end
+
+  @doc """
+  Exponentiation of a rational number by an integer
+  """
+  @spec pow_rational(a :: rational, n :: integer) :: rational
+  def pow_rational(a, n) do
+  end
+
+  @doc """
+  Exponentiation of a real number by a rational number
+  """
+  @spec pow_real(x :: float, n :: rational) :: float
+  def pow_real(x, n) do
+  end
+
+  @doc """
+  Reduce a rational number to its lowest terms
+  """
+  @spec reduce(a :: rational) :: rational
+  def reduce(a) do
+  end
+end

exercises/practice/rational-numbers/mix.exs

@@ -0,0 +1,28 @@
+defmodule RationalNumbers.MixProject do
+  use Mix.Project
+
+  def project do
+    [
+      app: :rational_numbers,
+      version: "0.1.0",
+      # elixir: "~> 1.8",
+      start_permanent: Mix.env() == :prod,
+      deps: deps()
+    ]
+  end
+
+  # Run "mix help compile.app" to learn about applications.
+  def application do
+    [
+      extra_applications: [:logger]
+    ]
+  end
+
+  # Run "mix help deps" to learn about dependencies.
+  defp deps do
+    [
+      # {:dep_from_hexpm, "~> 0.3.0"},
+      # {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"}
+    ]
+  end
+end