[New Exercise]: Complex Numbers (#516)

* Test template, but it's terrible

* A little cleaner

* Much simpler

* Add example

* Added append, decreased difficulty rating

* Add flattened_cases helper

bin/generator_help.cr

@@ -113,5 +113,25 @@ class GeneratorHelp
     "pending"
   end
 
+  def flattened_cases(cases : JSON::Any)
+    flattened_cases = [] of JSON::Any
+
+    cases.as_a.each do |cases|
+      if cases["cases"]?
+        cases["cases"].as_a.each do |cases|
+          if cases["cases"]?
+            flattened_cases.concat(cases["cases"].as_a)
+          else
+            flattened_cases << cases
+          end
+        end
+      else
+        flattened_cases << cases
+      end
+    end
+
+    flattened_cases
+  end
+
   ECR.def_to_s "./bin/templates/template.ecr"
 end

config.json

@@ -1067,6 +1067,15 @@
         "prerequisites": [],
         "difficulty": 4
       },
+      {
+        "slug": "complex-numbers",
+        "name": "Complex Numbers",
+        "uuid": "bc681ef9-c0ef-46bc-ac67-8720131161c0",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4,
+        "topics": []
+      },
       {
         "slug": "sum-of-multiples",
         "name": "Sum of Multiples",

exercises/practice/complex-numbers/.docs/instructions.append.md

@@ -0,0 +1,4 @@
+In this exercise you will need to add methods to an existing struct (`Number`).
+You can see an example of this in the Crystal documentation for [getters and setters][getters-and-setters]
+
+[getters-and-setters]: https://crystal-lang.org/reference/1.9/syntax_and_semantics/methods_and_instance_variables.html#getters-and-setters

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

@@ -0,0 +1,29 @@
+# Instructions
+
+A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
+
+`a` is called the real part and `b` is called the imaginary part of `z`.
+The conjugate of the number `a + b * i` is the number `a - b * i`.
+The absolute value of a complex number `z = a + b * i` is a real number `|z| = sqrt(a^2 + b^2)`. The square of the absolute value `|z|^2` is the result of multiplication of `z` by its complex conjugate.
+
+The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
+`(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`,
+`(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`.
+
+Multiplication result is by definition
+`(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`.
+
+The reciprocal of a non-zero complex number is
+`1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`.
+
+Dividing a complex number `a + i * b` by another `c + i * d` gives:
+`(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`.
+
+Raising e to a complex exponent can be expressed as `e^(a + i * b) = e^a * e^(i * b)`, the last term of which is given by Euler's formula `e^(i * b) = cos(b) + i * sin(b)`.
+
+Implement the following operations:
+
+- addition, subtraction, multiplication and division of two complex numbers,
+- conjugate, absolute value, exponent of a given complex number.
+
+Assume the programming language you are using does not have an implementation of complex numbers.

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

@@ -0,0 +1,17 @@
+{
+  "authors": ["ryanplusplus"],
+  "files": {
+    "solution": [
+      "src/complex_numbers.cr"
+    ],
+    "test": [
+      "spec/complex_numbers_spec.cr"
+    ],
+    "example": [
+      ".meta/src/example.cr"
+    ]
+  },
+  "blurb": "Implement complex numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Complex_number"
+}

exercises/practice/complex-numbers/.meta/src/example.cr

@@ -0,0 +1,84 @@
+class Complex
+  getter real, imaginary
+
+  def initialize(@real : Float64, @imaginary : Float64)
+  end
+
+  def +(other : Complex)
+    self.class.new(
+      @real + other.real,
+      @imaginary + other.imaginary
+    )
+  end
+
+  def +(f : Float64)
+    self + self.class.new(f, 0)
+  end
+
+  def -(other : Complex)
+    self.class.new(
+      @real - other.real,
+      @imaginary - other.imaginary
+    )
+  end
+
+  def -(f : Float64)
+    self - self.class.new(f, 0)
+  end
+
+  def *(other : Complex)
+    self.class.new(
+      @real * other.real - @imaginary * other.imaginary,
+      @real * other.imaginary + @imaginary * other.real
+    )
+  end
+
+  def *(f : Float64)
+    self * self.class.new(f, 0)
+  end
+
+  def /(other : Complex)
+    self.class.new(
+      (real * other.real + imaginary * other.imaginary) / (other.real ** 2 + other.imaginary ** 2),
+      (imaginary * other.real - real * other.imaginary) / (other.real ** 2 + other.imaginary ** 2)
+    )
+  end
+
+  def /(f : Float64)
+    self / self.class.new(f, 0)
+  end
+
+  def abs
+    Math.sqrt(real ** 2 + imaginary ** 2)
+  end
+
+  def conjugate
+    self.class.new(real, -imaginary)
+  end
+
+  def exp
+    self.class.new(Math.exp(real), 0) * self.class.new(Math.cos(imaginary), Math.sin(imaginary))
+  end
+
+  def ==(other : Complex)
+    (real - other.real).abs < 1e-9 && (imaginary - other.imaginary).abs < 1e-9
+  end
+end
+
+struct Number
+  def +(complex : Complex)
+    Complex.new(self, 0) + complex
+  end
+
+  def -(complex : Complex)
+    Complex.new(self, 0) - complex
+  end
+
+  def *(complex : Complex)
+    Complex.new(self, 0) * complex
+  end
+
+  def /(complex : Complex)
+    Complex.new(self, 0) / complex
+  end
+end

exercises/practice/complex-numbers/.meta/test_template.ecr

@@ -0,0 +1,61 @@
+require "spec"
+require "../src/*"
+
+<% property_map = {
+  ".real" => ".real",
+  ".imaginary" => ".imaginary",
+  ".abs" => ".abs",
+  ".conjugate" => ".conjugate",
+  ".exp" => ".exp",
+  ".add" => "+",
+  ".sub" => "-",
+  ".mul" => "*",
+  ".div" => "/"
+} %>
+
+<%
+complex_args = ->(json : JSON::Any) {
+  json
+    .as_a
+    .map(&.to_s)
+    .map(&.gsub("e", "Math::E"))
+    .map(&.gsub("pi", "Math::PI"))
+    .map(&.gsub("ln", "Math.log"))
+    .join(",")
+}
+%>
+
+describe <%= to_capitalized(@json["exercise"].to_s).inspect %> do
+    <% flattened_cases(@json["cases"]).each do |cases| %>
+        <%= status()%> "<%-= cases["description"] %>" do
+            <% if cases["input"]["z"]? %>
+                Complex.new(<%= complex_args.call(cases["input"]["z"]) %>)<%= property_map["." + cases["property"].to_s] -%>
+                .should eq <% -%>
+                <% if cases["expected"].as_a? -%>
+                    Complex.new(<%= complex_args.call(cases["expected"]) %>)<% -%>
+                <% else -%>
+                    <%= cases["expected"] -%>
+                <% end -%>
+            <% else %>
+                (<% -%>
+                <% if cases["input"]["z1"].as_a? -%>
+                    Complex.new(<%= complex_args.call(cases["input"]["z1"]) %>)<% -%>
+                <% else -%>
+                    <%= cases["input"]["z1"] -%><% -%>
+                <% end -%>
+                <%= property_map["." + cases["property"].to_s] -%><% -%>
+                    <% if cases["input"]["z2"].as_a? -%>
+                        Complex.new(<%= complex_args.call(cases["input"]["z2"]) %>)<% -%>
+                    <% else -%>
+                        <%= cases["input"]["z2"] -%><% -%>
+                    <% end -%>
+                ).should eq<% -%>
+                <% if cases["expected"].as_a? -%>
+                    Complex.new(<%= complex_args.call(cases["expected"]) %>)<% -%>
+                <% else -%>
+                    <%= cases["expected"] -%>
+                <% end -%>
+            <% end %>
+        end
+    <% end %>
+end

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

@@ -0,0 +1,130 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[9f98e133-eb7f-45b0-9676-cce001cd6f7a]
+description = "Real part -> Real part of a purely real number"
+
+[07988e20-f287-4bb7-90cf-b32c4bffe0f3]
+description = "Real part -> Real part of a purely imaginary number"
+
+[4a370e86-939e-43de-a895-a00ca32da60a]
+description = "Real part -> Real part of a number with real and imaginary part"
+
+[9b3fddef-4c12-4a99-b8f8-e3a42c7ccef6]
+description = "Imaginary part -> Imaginary part of a purely real number"
+
+[a8dafedd-535a-4ed3-8a39-fda103a2b01e]
+description = "Imaginary part -> Imaginary part of a purely imaginary number"
+
+[0f998f19-69ee-4c64-80ef-01b086feab80]
+description = "Imaginary part -> Imaginary part of a number with real and imaginary part"
+
+[a39b7fd6-6527-492f-8c34-609d2c913879]
+description = "Imaginary unit"
+
+[9a2c8de9-f068-4f6f-b41c-82232cc6c33e]
+description = "Arithmetic -> Addition -> Add purely real numbers"
+
+[657c55e1-b14b-4ba7-bd5c-19db22b7d659]
+description = "Arithmetic -> Addition -> Add purely imaginary numbers"
+
+[4e1395f5-572b-4ce8-bfa9-9a63056888da]
+description = "Arithmetic -> Addition -> Add numbers with real and imaginary part"
+
+[1155dc45-e4f7-44b8-af34-a91aa431475d]
+description = "Arithmetic -> Subtraction -> Subtract purely real numbers"
+
+[f95e9da8-acd5-4da4-ac7c-c861b02f774b]
+description = "Arithmetic -> Subtraction -> Subtract purely imaginary numbers"
+
+[f876feb1-f9d1-4d34-b067-b599a8746400]
+description = "Arithmetic -> Subtraction -> Subtract numbers with real and imaginary part"
+
+[8a0366c0-9e16-431f-9fd7-40ac46ff4ec4]
+description = "Arithmetic -> Multiplication -> Multiply purely real numbers"
+
+[e560ed2b-0b80-4b4f-90f2-63cefc911aaf]
+description = "Arithmetic -> Multiplication -> Multiply purely imaginary numbers"
+
+[4d1d10f0-f8d4-48a0-b1d0-f284ada567e6]
+description = "Arithmetic -> Multiplication -> Multiply numbers with real and imaginary part"
+
+[b0571ddb-9045-412b-9c15-cd1d816d36c1]
+description = "Arithmetic -> Division -> Divide purely real numbers"
+
+[5bb4c7e4-9934-4237-93cc-5780764fdbdd]
+description = "Arithmetic -> Division -> Divide purely imaginary numbers"
+
+[c4e7fef5-64ac-4537-91c2-c6529707701f]
+description = "Arithmetic -> Division -> Divide numbers with real and imaginary part"
+
+[c56a7332-aad2-4437-83a0-b3580ecee843]
+description = "Absolute value -> Absolute value of a positive purely real number"
+
+[cf88d7d3-ee74-4f4e-8a88-a1b0090ecb0c]
+description = "Absolute value -> Absolute value of a negative purely real number"
+
+[bbe26568-86c1-4bb4-ba7a-da5697e2b994]
+description = "Absolute value -> Absolute value of a purely imaginary number with positive imaginary part"
+
+[3b48233d-468e-4276-9f59-70f4ca1f26f3]
+description = "Absolute value -> Absolute value of a purely imaginary number with negative imaginary part"
+
+[fe400a9f-aa22-4b49-af92-51e0f5a2a6d3]
+description = "Absolute value -> Absolute value of a number with real and imaginary part"
+
+[fb2d0792-e55a-4484-9443-df1eddfc84a2]
+description = "Complex conjugate -> Conjugate a purely real number"
+
+[e37fe7ac-a968-4694-a460-66cb605f8691]
+description = "Complex conjugate -> Conjugate a purely imaginary number"
+
+[f7704498-d0be-4192-aaf5-a1f3a7f43e68]
+description = "Complex conjugate -> Conjugate a number with real and imaginary part"
+
+[6d96d4c6-2edb-445b-94a2-7de6d4caaf60]
+description = "Complex exponential function -> Euler's identity/formula"
+
+[2d2c05a0-4038-4427-a24d-72f6624aa45f]
+description = "Complex exponential function -> Exponential of 0"
+
+[ed87f1bd-b187-45d6-8ece-7e331232c809]
+description = "Complex exponential function -> Exponential of a purely real number"
+
+[08eedacc-5a95-44fc-8789-1547b27a8702]
+description = "Complex exponential function -> Exponential of a number with real and imaginary part"
+
+[d2de4375-7537-479a-aa0e-d474f4f09859]
+description = "Complex exponential function -> Exponential resulting in a number with real and imaginary part"
+
+[06d793bf-73bd-4b02-b015-3030b2c952ec]
+description = "Operations between real numbers and complex numbers -> Add real number to complex number"
+
+[d77dbbdf-b8df-43f6-a58d-3acb96765328]
+description = "Operations between real numbers and complex numbers -> Add complex number to real number"
+
+[20432c8e-8960-4c40-ba83-c9d910ff0a0f]
+description = "Operations between real numbers and complex numbers -> Subtract real number from complex number"
+
+[b4b38c85-e1bf-437d-b04d-49bba6e55000]
+description = "Operations between real numbers and complex numbers -> Subtract complex number from real number"
+
+[dabe1c8c-b8f4-44dd-879d-37d77c4d06bd]
+description = "Operations between real numbers and complex numbers -> Multiply complex number by real number"
+
+[6c81b8c8-9851-46f0-9de5-d96d314c3a28]
+description = "Operations between real numbers and complex numbers -> Multiply real number by complex number"
+
+[8a400f75-710e-4d0c-bcb4-5e5a00c78aa0]
+description = "Operations between real numbers and complex numbers -> Divide complex number by real number"
+
+[9a867d1b-d736-4c41-a41e-90bd148e9d5e]
+description = "Operations between real numbers and complex numbers -> Divide real number by complex number"