[New Exercise]: Pythagorean Triplet

config.json

@@ -660,6 +660,14 @@
         "prerequisites": [],
         "difficulty": 3
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "7d3309b4-8efb-4357-8893-c654ccee7e79",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 3
+      },
       {
         "slug": "ocr-numbers",
         "name": "OCR Numbers",

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/PythagoreanTriplet.example.ps1

@@ -0,0 +1,56 @@
+Function Get-PythagoreanTriplet() {
+    <#
+    .SYNOPSIS
+    Given input integer N, find all Pythagorean triplets for which 'a + b + c = N'.
+
+    .DESCRIPTION
+    Given an integer, find all the possible Pythagorean triplets whose sum is equal to that integer.
+    Return the array of Pythagorean triplets in sorted ascending order.
+
+    A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which:
+    a² + b² = c²
+    a < b < c
+
+    .PARAMETER Number
+    The sum of a Pythagorean triplet
+
+    .EXAMPLE
+    Get-PythagoreanTriplet -Sum 12
+    Return: @( ,@(3, 4, 5))
+    #>
+    [CmdletBinding()]
+    Param(
+        [int]$Sum
+    )
+    # Logic : If a is at maximum, it still less than b, and b less than c. So c at mimimum but be around N/3
+    # For a + b + c = N and a² + b² = c² to be valid, c at maximum cant be larger than N/2
+    $rangeOfc = [math]::Floor($Sum / 3)..[math]::Floor($Sum / 2)
+    $triplets = @()
+
+    foreach ($c in $rangeOfc) {
+        $abSum = $Sum - $c
+        $abProd =  [math]::Floor(($abSum * $abSum - $c * $c) / 2)
+        if ($abProd -gt 0) {
+            $a, $b = Get-AB $abSum $abProd
+            $validTriple = ($a * $a + $b * $b) -eq ($c * $c)
+            if ($a -and $b -and $validTriple) {
+                $triplets += ,@($a, $b, $c)
+            }
+        }
+    }
+    $triplets | Sort-Object { $_[0] }
+}
+
+function Get-AB($abSum, $abProd) {
+    <#
+    .DESCRIPTION
+    Helper function using the identity (x+y)2−4xy=(x−y)2 aka ab_sum*2−4*ab_prod = (x−y)^2
+    to find a and b
+    #>
+    $abDifSqr = [math]::Pow($abSum, 2) - 4 * $abProd
+    if ($abDifSqr -gt 0) {
+        $abDif = [math]::Floor([math]::Sqrt($abDifSqr))
+        $b, $a = [math]::Floor(($abSum + $abDif) / 2) , [math]::Floor(($abSum - $abDif) / 2)
+        $a, $b
+    }
+}

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

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glaxxie"
+  ],
+  "files": {
+    "solution": [
+      "PythagoreanTriplet.ps1"
+    ],
+    "test": [
+      "PythagoreanTriplet.tests.ps1"
+    ],
+    "example": [
+      ".meta/PythagoreanTriplet.example.ps1"
+    ]
+  },
+  "blurb": "There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product a * b * c.",
+  "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/PythagoreanTriplet.ps1

@@ -0,0 +1,26 @@
+Function Get-PythagoreanTriplet() {
+    <#
+    .SYNOPSIS
+    Given input integer N, find all Pythagorean triplets for which 'a + b + c = N'.
+
+    .DESCRIPTION
+    Given an integer, find all the possible Pythagorean triplets whose sum is equal to that integer.
+    Return the array of Pythagorean triplets in sorted ascending order.
+
+    A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which:
+    a² + b² = c²
+    a < b < c
+
+    .PARAMETER Number
+    The sum of a Pythagorean triplet
+
+    .EXAMPLE
+    Get-PythagoreanTriplet -Sum 12
+    Return: @( ,@(3, 4, 5))
+    #>
+    [CmdletBinding()]
+    Param(
+        [int]$Sum
+    )
+    Throw "Please implement this function"
+}

exercises/practice/pythagorean-triplet/PythagoreanTriplet.tests.ps1

@@ -0,0 +1,68 @@
+BeforeAll {
+    . "./PythagoreanTriplet.ps1"
+}
+
+Describe "PythagoreanTriplet test cases" {
+    It "triplets whose sum is 12" {
+        $got  = Get-PythagoreanTriplet -Sum 12
+        $want = @( ,@(3, 4, 5))
+
+        ,$got | Should -BeExactly $want
+    }
+
+    It "triplets whose sum is 108" {
+        $got  = Get-PythagoreanTriplet -Sum 108
+        $want = @( ,@(27, 36, 45))
+
+        ,$got | Should -BeExactly $want
+    }
+
+    It "triplets whose sum is 1000" {
+        $got  = Get-PythagoreanTriplet -Sum 1000
+        $want = @( ,@(200, 375, 425))
+
+        ,$got | Should -BeExactly $want
+    }
+
+    It "no matching triplets for 1001" {
+        $got  = Get-PythagoreanTriplet -Sum 1001
+
+        $got | Should -BeNullOrEmpty
+    }
+
+    It "returns all matching triplets" {
+        $got  = Get-PythagoreanTriplet -Sum 90
+        $want = @( @(9, 40, 41), @(15, 36, 39))
+
+        $got | Should -BeExactly $want
+    }
+
+    It "several matching triplets" {
+        $got  = Get-PythagoreanTriplet -Sum 840
+        $want = @(
+            @(40, 399, 401),
+            @(56, 390, 394),
+            @(105, 360, 375),
+            @(120, 350, 370),
+            @(140, 336, 364),
+            @(168, 315, 357),
+            @(210, 280, 350),
+            @(240, 252, 348)
+        )
+
+        $got | Should -BeExactly $want
+    }
+
+    It "triplets for large number" {
+        $got  = Get-PythagoreanTriplet -Sum 30000
+        $want = @(
+            @(1200, 14375, 14425),
+            @(1875, 14000, 14125),
+            @(5000, 12000, 13000),
+            @(6000, 11250, 12750),
+            @(7500, 10000, 12500)
+        )
+
+        $got | Should -BeExactly $want
+    }
+}