Add difference-of-squares (exercism#152)

config.json

@@ -116,6 +116,14 @@
         "prerequisites": [],
         "difficulty": 2
       },
+      {
+        "slug": "difference-of-squares",
+        "name": "Difference of Squares",
+        "uuid": "d65ce143-9c7f-4e5d-86d1-8b3fef0b4404",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 2
+      },
       {
         "slug": "eliuds-eggs",
         "name": "Eliud's Eggs",

exercises/practice/difference-of-squares/.docs/instructions.md

@@ -0,0 +1,14 @@
+# Instructions
+
+Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.
+
+The square of the sum of the first ten natural numbers is
+(1 + 2 + ... + 10)² = 55² = 3025.
+
+The sum of the squares of the first ten natural numbers is
+1² + 2² + ... + 10² = 385.
+
+Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.
+
+You are not expected to discover an efficient solution to this yourself from first principles; research is allowed, indeed, encouraged.
+Finding the best algorithm for the problem is a key skill in software engineering.

exercises/practice/difference-of-squares/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "src/DifferenceOfSquares.idr"
+    ],
+    "test": [
+      "test/src/Main.idr"
+    ],
+    "example": [
+      "example/DifferenceOfSquares.idr"
+    ]
+  },
+  "blurb": "Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.",
+  "source": "Problem 6 at Project Euler",
+  "source_url": "https://projecteuler.net/problem=6"
+}

exercises/practice/difference-of-squares/.meta/tests.toml

@@ -0,0 +1,37 @@
+# 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.
+
+[e46c542b-31fc-4506-bcae-6b62b3268537]
+description = "Square the sum of the numbers up to the given number -> square of sum 1"
+
+[9b3f96cb-638d-41ee-99b7-b4f9c0622948]
+description = "Square the sum of the numbers up to the given number -> square of sum 5"
+
+[54ba043f-3c35-4d43-86ff-3a41625d5e86]
+description = "Square the sum of the numbers up to the given number -> square of sum 100"
+
+[01d84507-b03e-4238-9395-dd61d03074b5]
+description = "Sum the squares of the numbers up to the given number -> sum of squares 1"
+
+[c93900cd-8cc2-4ca4-917b-dd3027023499]
+description = "Sum the squares of the numbers up to the given number -> sum of squares 5"
+
+[94807386-73e4-4d9e-8dec-69eb135b19e4]
+description = "Sum the squares of the numbers up to the given number -> sum of squares 100"
+
+[44f72ae6-31a7-437f-858d-2c0837adabb6]
+description = "Subtract sum of squares from square of sums -> difference of squares 1"
+
+[005cb2bf-a0c8-46f3-ae25-924029f8b00b]
+description = "Subtract sum of squares from square of sums -> difference of squares 5"
+
+[b1bf19de-9a16-41c0-a62b-1f02ecc0b036]
+description = "Subtract sum of squares from square of sums -> difference of squares 100"

exercises/practice/difference-of-squares/difference-of-squares.ipkg

@@ -0,0 +1,3 @@
+package difference-of-squares
+modules = DifferenceOfSquares
+sourcedir = "src"

exercises/practice/difference-of-squares/example/DifferenceOfSquares.idr

@@ -0,0 +1,15 @@
+module DifferenceOfSquares
+
+export
+squareOfSum : Integer -> Integer
+squareOfSum number = square sum
+  where sum = div (number * (number + 1)) 2
+        square n = n * n
+
+export
+sumOfSquares : Integer -> Integer
+sumOfSquares number = div (number * (number + 1) * (number + number + 1)) 6
+
+export
+differenceOfSquares : Integer -> Integer
+differenceOfSquares number = (squareOfSum number) - (sumOfSquares number)

exercises/practice/difference-of-squares/pack.toml

@@ -0,0 +1,10 @@
+[custom.all.difference-of-squares]
+type = "local"
+path = "."
+ipkg = "difference-of-squares.ipkg"
+test = "test/test.ipkg"
+
+[custom.all.difference-of-squares-test]
+type = "local"
+path = "test"
+ipkg = "test.ipkg"

exercises/practice/difference-of-squares/src/DifferenceOfSquares.idr

@@ -0,0 +1,13 @@
+module DifferenceOfSquares
+
+export
+squareOfSum : Integer -> Integer
+squareOfSum number = ?squareOfSum_rhs
+
+export
+sumOfSquares : Integer -> Integer
+sumOfSquares number = ?sumOfSquares_rhs
+
+export
+differenceOfSquares : Integer -> Integer
+differenceOfSquares number = ?differenceOfSquares_rhs

exercises/practice/difference-of-squares/test/src/Main.idr

@@ -0,0 +1,28 @@
+module Main
+
+import System
+import Tester
+import Tester.Runner
+
+import DifferenceOfSquares
+
+tests : List Test
+tests =
+  [ test "square of sum 1"           (assertEq (squareOfSum 1) 1)
+  , test "square of sum 5"           (assertEq (squareOfSum 5) 225)
+  , test "square of sum 100"         (assertEq (squareOfSum 100) 25502500)
+  , test "sum of squares 1"          (assertEq (sumOfSquares 1) 1)
+  , test "sum of squares 5"          (assertEq (sumOfSquares 5) 55)
+  , test "sum of squares 100"        (assertEq (sumOfSquares 100) 338350)
+  , test "difference of squares 1"   (assertEq (differenceOfSquares 1) 0)
+  , test "difference of squares 5"   (assertEq (differenceOfSquares 5) 170)
+  , test "difference of squares 100" (assertEq (differenceOfSquares 100) 25164150)
+  ]
+
+export
+main : IO ()
+main = do
+  success <- runTests tests
+  if success
+     then putStrLn "All tests passed"
+     else exitFailure

exercises/practice/difference-of-squares/test/test.ipkg

@@ -0,0 +1,6 @@
+package difference-of-squares-test
+depends = difference-of-squares
+  , tester
+main = Main
+executable = "difference-of-squares-test"
+sourcedir = "src"

generators/exercises/difference_of_squares.py

@@ -0,0 +1,6 @@
+
+def generate_test(case):
+    property = case["property"]
+    expected = case["expected"]
+    number = case["input"]["number"]
+    return f'assertEq ({property} {number}) {expected}'