Add pythagorean-triplet exercise

config.json

@@ -315,6 +315,17 @@
         "difficulty": 1,
         "topics": []
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "203470a2-f80c-4d6c-8ea4-7d09d7bfb509",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5,
+        "topics": [
+          "math"
+        ]
+      },
       {
         "slug": "roman-numerals",
         "name": "Roman Numerals",

exercises/practice/pythagorean-triplet/.docs/instructions.md

@@ -0,0 +1,23 @@
+# Instructions
+
+A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,
+
+```text
+a² + b² = c²
+```
+
+and such that,
+
+```text
+a < b < c
+```
+
+For example,
+
+```text
+3² + 4² = 5².
+```
+
+Given an input integer N, find all Pythagorean triplets for which `a + b + c = N`.
+
+For example, with N = 1000, there is exactly one Pythagorean triplet for which `a + b + c = 1000`: `{200, 375, 425}`.

exercises/practice/pythagorean-triplet/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "pythagorean-triplet.sml"
+    ],
+    "test": [
+      "test.sml"
+    ],
+    "example": [
+      ".meta/example.sml"
+    ]
+  },
+  "blurb": "There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the triplet.",
+  "source": "Problem 9 at Project Euler",
+  "source_url": "https://projecteuler.net/problem=9"
+}

exercises/practice/pythagorean-triplet/.meta/example.sml

@@ -0,0 +1,25 @@
+(* For every Pythagorean triplet with total a + b + c = n,
+ * a² + b² = c²
+ * <=> a² + b² = (n - a - b)², substituting c
+ * <=> 0 = n² - 2*n*a - 2*n*b + 2*a*b
+ * <=> (2*n - 2*a) b = (n² - 2*n*a)
+ * <=> b = (n² - 2*n*a) / (2*n - 2*a)
+ *
+ * The denominator is never 0, as perimeter exceeds a side length.
+ *)
+fun tripletsWithSum (n: int): (int * int * int) list =
+  let
+    fun recurse (a: int): (int * int * int) list =
+      let
+        val numerator = n * (n - 2 * a)
+        val denominator = 2 * (n - a)
+        val b = numerator div denominator
+      in
+        if b <= a then nil
+        else if numerator mod denominator <> 0 then recurse (a + 1)
+        else (a, b, n - a - b) :: recurse (a + 1)
+      end
+  in
+    if n < 2 then nil
+    else recurse 1
+  end

exercises/practice/pythagorean-triplet/.meta/tests.toml

@@ -0,0 +1,31 @@
+# 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.
+
+[a19de65d-35b8-4480-b1af-371d9541e706]
+description = "triplets whose sum is 12"
+
+[48b21332-0a3d-43b2-9a52-90b2a6e5c9f5]
+description = "triplets whose sum is 108"
+
+[dffc1266-418e-4daa-81af-54c3e95c3bb5]
+description = "triplets whose sum is 1000"
+
+[5f86a2d4-6383-4cce-93a5-e4489e79b186]
+description = "no matching triplets for 1001"
+
+[bf17ba80-1596-409a-bb13-343bdb3b2904]
+description = "returns all matching triplets"
+
+[9d8fb5d5-6c6f-42df-9f95-d3165963ac57]
+description = "several matching triplets"
+
+[f5be5734-8aa0-4bd1-99a2-02adcc4402b4]
+description = "triplets for large number"

exercises/practice/pythagorean-triplet/pythagorean-triplet.sml

@@ -0,0 +1,2 @@
+fun tripletsWithSum (n: int): (int * int * int) list =
+  raise Fail "'tripletsWithSum' is not implemented"

exercises/practice/pythagorean-triplet/test.sml

@@ -0,0 +1,33 @@
+(* version 1.0.0 *)
+
+use "testlib.sml";
+use "pythagorean-triplet.sml";
+
+infixr |>
+fun x |> f = f x
+
+val testsuite =
+  describe "pythagorean-triplet" [
+    test "triplets whose sum is 12"
+      (fn _ => tripletsWithSum 12 |> Expect.equalTo [(3, 4, 5)]),
+
+    test "triplets whose sum is 108"
+      (fn _ => tripletsWithSum 108 |> Expect.equalTo [(27, 36, 45)]),
+
+    test "triplets whose sum is 1000"
+      (fn _ => tripletsWithSum 1000 |> Expect.equalTo [(200, 375, 425)]),
+
+    test "no matching triplets for 1001"
+      (fn _ => tripletsWithSum 1001 |> Expect.equalTo []),
+
+    test "returns all matching triplets"
+      (fn _ => tripletsWithSum 90 |> Expect.equalTo [(9, 40, 41), (15, 36, 39)]),
+
+    test "several matching triplets"
+      (fn _ => tripletsWithSum 840 |> Expect.equalTo [(40, 399, 401), (56, 390, 394), (105, 360, 375), (120, 350, 370), (140, 336, 364), (168, 315, 357), (210, 280, 350), (240, 252, 348)]),
+
+    test "triplets for large number"
+      (fn _ => tripletsWithSum 30000 |> Expect.equalTo [(1200, 14375, 14425), (1875, 14000, 14125), (5000, 12000, 13000), (6000, 11250, 12750), (7500, 10000, 12500)])
+  ]
+
+val _ = Test.run testsuite

exercises/practice/pythagorean-triplet/testlib.sml

@@ -0,0 +1,160 @@
+structure Expect =
+struct
+  datatype expectation = Pass | Fail of string * string
+
+  local
+    fun failEq b a =
+      Fail ("Expected: " ^ b, "Got: " ^ a)
+
+    fun failExn b a =
+      Fail ("Expected: " ^ b, "Raised: " ^ a)
+
+    fun exnName (e: exn): string = General.exnName e
+  in
+    fun truthy a =
+      if a
+      then Pass
+      else failEq "true" "false"
+
+    fun falsy a =
+      if a
+      then failEq "false" "true"
+      else Pass
+
+    fun equalTo b a = 
+      if a = b
+      then Pass
+      else failEq (PolyML.makestring b) (PolyML.makestring a)
+
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
+      then Pass
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
+
+    fun anyError f =
+      (
+        f ();
+        failExn "an exception" "Nothing"
+      ) handle _ => Pass
+
+    fun error e f =
+      (
+        f ();
+        failExn (exnName e) "Nothing"
+      ) handle e' => if exnMessage e' = exnMessage e
+                     then Pass
+                     else failExn (exnMessage e) (exnMessage e')
+  end
+end
+
+structure TermColor =
+struct
+  datatype color = Red | Green | Yellow | Normal
+
+  fun f Red    = "\027[31m"
+    | f Green  = "\027[32m"
+    | f Yellow = "\027[33m"
+    | f Normal = "\027[0m"
+
+  fun colorize color s = (f color) ^ s ^ (f Normal)
+
+  val redit = colorize Red
+
+  val greenit = colorize Green
+
+  val yellowit = colorize Yellow
+end
+
+structure Test =
+struct
+  datatype testnode = TestGroup of string * testnode list
+                    | Test of string * (unit -> Expect.expectation)
+
+  local
+    datatype evaluation = Success of string
+                        | Failure of string * string * string
+                        | Error of string * string
+
+    fun indent n s = (implode (List.tabulate (n, fn _ => #" "))) ^ s
+
+    fun fmt indentlvl ev =
+      let
+        val check = TermColor.greenit "\226\156\148 " (* ✔ *)
+        val cross = TermColor.redit "\226\156\150 "   (* ✖ *)
+        val indentlvl = indentlvl * 2
+      in
+      case ev of
+        Success descr => indent indentlvl (check ^ descr)
+      | Failure (descr, exp, got) =>
+          String.concatWith "\n" [indent indentlvl (cross ^ descr),
+                                  indent (indentlvl + 2) exp,
+                                  indent (indentlvl + 2) got]
+      | Error (descr, reason) =>
+          String.concatWith "\n" [indent indentlvl (cross ^ descr),
+                                  indent (indentlvl + 2) (TermColor.redit reason)]
+      end
+
+    fun eval (TestGroup _) = raise Fail "Only a 'Test' can be evaluated"
+      | eval (Test (descr, thunk)) =
+          (
+            case thunk () of
+              Expect.Pass   => ((1, 0, 0), Success descr)
+            | Expect.Fail (s, s') => ((0, 1, 0), Failure (descr, s, s'))
+          )
+          handle e => ((0, 0, 1), Error (descr, "Unexpected error: " ^ exnMessage e))
+
+    fun flatten depth testnode =
+      let
+        fun sum (x, y, z) (a, b, c) = (x + a, y + b, z + c)
+
+        fun aux (t, (counter, acc)) =
+          let
+            val (counter', texts) = flatten (depth + 1) t
+          in
+            (sum counter' counter, texts :: acc)
+          end
+      in
+        case testnode of
+          TestGroup (descr, ts) =>
+            let
+              val (counter, texts) = foldr aux ((0, 0, 0), []) ts
+            in
+              (counter, (indent (depth * 2) descr) :: List.concat texts)
+            end
+        | Test _ =>
+            let
+              val (counter, evaluation) = eval testnode
+            in
+              (counter, [fmt depth evaluation])
+            end
+      end
+
+    fun println s = print (s ^ "\n")
+  in
+    fun run suite =
+      let
+        val ((succeeded, failed, errored), texts) = flatten 0 suite
+
+        val summary = String.concatWith ", " [
+          TermColor.greenit ((Int.toString succeeded) ^ " passed"),
+          TermColor.redit ((Int.toString failed) ^ " failed"),
+          TermColor.redit ((Int.toString errored) ^ " errored"),
+          (Int.toString (succeeded + failed + errored)) ^ " total"
+        ]
+
+        val status = if failed = 0 andalso errored = 0
+                     then OS.Process.success
+                     else OS.Process.failure
+
+      in
+        List.app println texts;
+        println "";
+        println ("Tests: " ^ summary);
+        OS.Process.exit status
+      end
+  end
+end
+
+fun describe description tests = Test.TestGroup (description, tests)
+fun test description thunk = Test.Test (description, thunk)