Add pythagorean-triplet exercise

config.json

@@ -565,6 +565,17 @@
           "strings"
         ]
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "f33d976d-5189-4fcb-b0ac-42879a1067bf",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5,
+        "topics": [
+          "math"
+        ]
+      },
       {
         "slug": "rail-fence-cipher",
         "name": "Rail Fence Cipher",

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.el"
+    ],
+    "test": [
+      "pythagorean-triplet-test.el"
+    ],
+    "example": [
+      ".meta/example.el"
+    ]
+  },
+  "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.el

@@ -0,0 +1,30 @@
+;;; pythagorean-triplet.el --- Pythagorean Triplet (exercism)  -*- lexical-binding: t; -*-
+
+;;; Commentary:
+
+; 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)
+
+;;; Code:
+
+(require 'cl-lib)
+
+(defun triplets-with-sum (n)
+  (cl-labels
+    ((recur (start)
+      (cl-loop for a from start
+        for numerator = (* n (- n a a))
+        for denominator = (* 2 (- n a))
+        for b = (/ numerator denominator)
+        always (< a b)
+        until (= 0 (% numerator denominator))
+        finally return (cons (list a b (- n a b)) (recur (1+ a))))))
+    (unless (< n 2)
+      (recur 1))))
+
+(provide 'pythagorean-triplet)
+;;; pythagorean-triplet.el ends here

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-test.el

@@ -0,0 +1,53 @@
+;;; pythagorean-triplet-test.el --- Tests for Pythagorean Triplet (exercism)  -*- lexical-binding: t; -*-
+
+;;; Commentary:
+
+;;; Code:
+
+(load-file "pythagorean-triplet.el")
+(declare-function triplets-with-sum "pythagorean-triplet.el" (n))
+
+
+(ert-deftest triplets-whose-sum-is-12 ()
+  (should (equal '((3 4 5)) (triplets-with-sum 12))))
+
+
+(ert-deftest triplets-whose-sum-is-108 ()
+  (should (equal '((27 36 45)) (triplets-with-sum 108))))
+
+
+(ert-deftest triplets-whose-sum-is-1000 ()
+  (should (equal '((200 375 425)) (triplets-with-sum 1000))))
+
+
+(ert-deftest no-matching-triplets-for-1001 ()
+  (should (equal '() (triplets-with-sum 1001))))
+
+
+(ert-deftest returns-all-matching-triplets ()
+  (should (equal '((9 40 41) (15 36 39)) (triplets-with-sum 90))))
+
+
+(ert-deftest several-matching-triplets ()
+  (should (equal '((40 399 401)
+                   (56 390 394)
+                   (105 360 375)
+                   (120 350 370)
+                   (140 336 364)
+                   (168 315 357)
+                   (210 280 350)
+                   (240 252 348))
+                 (triplets-with-sum 840))))
+
+
+(ert-deftest triplets-for-large-number ()
+  (should (equal '((1200 14375 14425)
+                   (1875 14000 14125)
+                   (5000 12000 13000)
+                   (6000 11250 12750)
+                   (7500 10000 12500))
+                 (triplets-with-sum 30000))))
+
+
+(provide 'pythagorean-triplet-test)
+;;; pythagorean-triplet-test.el ends here

exercises/practice/pythagorean-triplet/pythagorean-triplet.el

@@ -0,0 +1,13 @@
+;;; pythagorean-triplet.el --- Pythagorean Triplet (exercism)  -*- lexical-binding: t; -*-
+
+;;; Commentary:
+
+;;; Code:
+
+
+(defun triplets-with-sum (n)
+  (error "Delete this S-Expression and write your own implementation"))
+
+
+(provide 'pythagorean-triplet)
+;;; pythagorean-triplet.el ends here