Add pythagorean-triplet exercise (#263)

config.json

@@ -554,6 +554,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "dc415515-ad72-41a3-8d42-a7d976618848",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "scrabble-score",
         "name": "Scrabble Score",

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": [
+      "source/pythagorean_triplet.d"
+    ],
+    "test": [
+      "source/pythagorean_triplet.d"
+    ],
+    "example": [
+      "example/pythagorean_triplet.d"
+    ]
+  },
+  "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/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/dub.sdl

@@ -0,0 +1,2 @@
+name "pythagorean-triplet"
+buildRequirements "disallowDeprecations"

exercises/practice/pythagorean-triplet/example/pythagorean_triplet.d

@@ -0,0 +1,41 @@
+module pythagorean_triplet;
+
+struct Triplet {
+    uint a;
+    uint b;
+    uint c;
+}
+
+// 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)
+
+pure Triplet[] tripletsWithSum(uint n)
+{
+    Triplet[] result;
+    if (n < 2)
+    {
+        return result;
+    }
+
+    for (uint a = 1;;++a)
+    {
+        uint numerator = n * (n - 2 * a);
+        uint denominator = 2 * (n - a);
+        uint b = numerator / denominator;
+        if (b <= a)
+        {
+            break;
+        }
+        if (numerator % denominator != 0)
+        {
+            continue;
+        }
+        uint c = n - a - b;
+        result ~= Triplet(a, b, c);
+    }
+    return result;
+}

exercises/practice/pythagorean-triplet/source/pythagorean_triplet.d

@@ -0,0 +1,87 @@
+module pythagorean_triplet;
+
+struct Triplet {
+    uint a;
+    uint b;
+    uint c;
+}
+
+pure Triplet[] tripletsWithSum(uint n)
+{
+    // implement this function
+}
+
+unittest
+{
+    immutable int allTestsEnabled = 0;
+
+    // Triplets whose sum is 12
+    {
+        Triplet[] expected = [
+            Triplet(3, 4, 5),
+        ];
+        assert(tripletsWithSum(12) == expected);
+    }
+
+    static if (allTestsEnabled)
+    {
+        // Triplets whose sum is 108
+        {
+            Triplet[] expected = [
+                Triplet(27, 36, 45),
+            ];
+            assert(tripletsWithSum(108) == expected);
+        }
+
+        // Triplets whose sum is 1000
+        {
+            Triplet[] expected = [
+                Triplet(200, 375, 425),
+            ];
+            assert(tripletsWithSum(1000) == expected);
+        }
+
+        // No matching triplets for 1001
+        {
+            Triplet[] expected = [
+            ];
+            assert(tripletsWithSum(1001) == expected);
+        }
+
+        // Returns all matching triplets
+        {
+            Triplet[] expected = [
+                Triplet(9, 40, 41),
+                Triplet(15, 36, 39),
+            ];
+            assert(tripletsWithSum(90) == expected);
+        }
+
+        // Several matching triplets
+        {
+            Triplet[] expected = [
+                Triplet(40, 399, 401),
+                Triplet(56, 390, 394),
+                Triplet(105, 360, 375),
+                Triplet(120, 350, 370),
+                Triplet(140, 336, 364),
+                Triplet(168, 315, 357),
+                Triplet(210, 280, 350),
+                Triplet(240, 252, 348),
+            ];
+            assert(tripletsWithSum(840) == expected);
+        }
+
+        // Triplets for large number
+        {
+            Triplet[] expected = [
+                Triplet(1200, 14375, 14425),
+                Triplet(1875, 14000, 14125),
+                Triplet(5000, 12000, 13000),
+                Triplet(6000, 11250, 12750),
+                Triplet(7500, 10000, 12500),
+            ];
+            assert(tripletsWithSum(30000) == expected);
+        }
+    }
+}