Add pythagorean-triplet exercise (#58)

Author: keiravillekode

config.json

@@ -390,6 +390,14 @@
         "prerequisites": [],
         "difficulty": 6
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "5fbba379-44b1-445d-b2c2-7191e4706fae",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
+      },
       {
         "slug": "book-store",
         "name": "Book Store",

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

@@ -0,0 +1,23 @@
+# Description
+
+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/.docs/introduction.md

@@ -0,0 +1,19 @@
+# Introduction
+
+You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles.
+One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project.
+The letter reads:
+
+> Dear Mathematician,
+>
+> I need your help.
+> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c².
+> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N.
+> Calculating these triplets by hand would take me years, but I hear you are more than up to the task.
+>
+> Time is of the essence.
+> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem.
+
+Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition.
+Your work could have far-reaching implications, unlocking new possibilities in science and engineering.
+Can you rise to the challenge and make history?

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

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "pythagorean_triplet.fut"
+    ],
+    "test": [
+      "test.fut"
+    ],
+    "example": [
+      ".meta/example.fut"
+    ]
+  },
+  "blurb": "Given an integer N, find all Pythagorean triplets for which a + b + c = N.",
+  "source": "A variation of Problem 9 from Project Euler",
+  "source_url": "https://projecteuler.net/problem=9"
+}

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

@@ -0,0 +1,11 @@
+let triplets_with_sum (n: i32): [][3]i32 =
+  let (_, _, result) = loop (a, b, result) = (0, n / 2, []) while a < b do
+    let a2 = a + 1
+    let numerator = n * (n - 2 * a2)
+    let denominator = 2 * (n - a2)
+    let b2 = numerator / denominator
+    in
+      if a2 >= b2 || numerator % denominator != 0 then (a2, b2, result) else
+      (a2, b2, result ++ [[a2, b2, n - a2 - b2]])
+  in
+    result

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.fut

@@ -0,0 +1 @@
+let triplets_with_sum (n: i32): [][3]i32 = ???

exercises/practice/pythagorean-triplet/test.fut

@@ -0,0 +1,39 @@
+import "pythagorean_triplet"
+
+-- triplets whose sum is 12
+-- ==
+-- input { 12 }
+-- output { [[3, 4, 5]] }
+
+-- triplets whose sum is 108
+-- ==
+-- input { 108 }
+-- output { [[27, 36, 45]] }
+
+-- triplets whose sum is 1000
+-- ==
+-- input { 1000 }
+-- output { [[200, 375, 425]] }
+
+-- no matching triplets for 1001
+-- ==
+-- input { 1001 }
+-- output { empty([0][3]i32) }
+
+-- returns all matching triplets
+-- ==
+-- input { 90 }
+-- output { [[9, 40, 41], [15, 36, 39]] }
+
+-- several matching triplets
+-- ==
+-- input { 840 }
+-- output { [[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 for large number
+-- ==
+-- input { 30000 }
+-- output { [[1200, 14375, 14425], [1875, 14000, 14125], [5000, 12000, 13000], [6000, 11250, 12750], [7500, 10000, 12500]] }
+
+let main (n: i32): [][3]i32 =
+  triplets_with_sum n