Add pythagorean-triplet exercise (#263)

config.json

@@ -505,6 +505,17 @@
         "prerequisites": [],
         "difficulty": 4
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "548fa68b-98ff-4c3f-87ae-ef3a0cc605c1",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6,
+        "topics": [
+          "math"
+        ]
+      },
       {
         "slug": "all-your-base",
         "name": "All Your Base",

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

@@ -0,0 +1,6 @@
+# Hints
+
+## General
+
+- The `$t0-9` registers can be used to temporarily store values
+- The instructions specify which registers are used as input and output

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

@@ -0,0 +1,12 @@
+# Instructions append
+
+## Registers
+
+| Register | Usage        | Type    | Description                  |
+| -------- | ------------ | ------- | ---------------------------- |
+| `$a0`    | input        | integer | N, sum of sides of triangle  |
+| `$a1`    | input/output | address | a values                     |
+| `$a2`    | input/output | address | b values                     |
+| `$a3`    | input/output | address | c values                     |
+| `$v0`    | output       | integer | number of triplets           |
+| `$t0-9`  | temporary    | any     | for temporary storage        |

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": [
+      "impl.mips"
+    ],
+    "test": [
+      "runner.mips"
+    ],
+    "example": [
+      ".meta/example.mips"
+    ]
+  },
+  "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.mips

@@ -0,0 +1,59 @@
+# | Register | Usage        | Type    | Description                                  |
+# | -------- | ------------ | ------- | -------------------------------------------- |
+# | `$a0`    | input        | integer | N, sum of sides of triangle                  |
+# | `$a1`    | input/output | address | a values                                     |
+# | `$a2`    | input/output | address | b values                                     |
+# | `$a3`    | input/output | address | c values                                     |
+# | `$v0`    | output       | integer | number of triplets                           |
+# | `$t0`    | temporary    | address | start of a values                            |
+# | `$t1`    | temporary    | integer | a                                            |
+# | `$t2`    | temporary    | integer | b                                            |
+# | `$t3`    | temporary    | integer | c                                            |
+# | `$t5`    | temporary    | integer | remainder                                    |
+# | `$t6`    | temporary    | integer | numerator                                    |
+# | `$t7`    | temporary    | integer | denominator                                  |
+
+# 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 N exceeds a side length.
+
+.globl triplets_with_sum
+
+triplets_with_sum:
+        move    $t0, $a1                # start of a values
+        blt     $a0, 2, return          # Stop immediately if N < 2
+        move    $t1, $zero              # Initialize a
+        j       increment_a
+
+check_remainder:
+        mfhi    $t5                     # remainder
+        bnez    $t5, increment_a
+        sub     $t3, $a0, $t1
+        sub     $t3, $t3, $t2           # c = N - a - b
+
+        sw      $t1, 0($a1)
+        sw      $t2, 0($a2)
+        sw      $t3, 0($a3)
+        addi    $a1, $a1, 4             # Increment pointer for a
+        addi    $a2, $a2, 4             # Increment pointer for b
+        addi    $a3, $a3, 4             # Increment pointer for c
+
+increment_a:
+        addi    $t1, $t1, 1
+        sub     $t7, $a0, $t1           # N - a
+        sub     $t6, $t7, $t1           # N - 2*a
+        sll     $t7, $t7, 1             # denominator = 2*N - 2*a
+        mulu    $t6, $a0, $t6           # numerator = N² - 2*N*a
+        div     $t6, $t7
+        mflo    $t2                     # b
+        bgt     $t2, $t1, check_remainder # loop while b > a
+
+return:
+        sub     $v0, $a1, $t0           # compute number of triplets
+        srl     $v0, $v0, 2
+        jr      $ra

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/impl.mips

@@ -0,0 +1,13 @@
+# | Register | Usage        | Type    | Description                                  |
+# | -------- | ------------ | ------- | -------------------------------------------- |
+# | `$a0`    | input        | integer | N, sum of sides of triangle                  |
+# | `$a1`    | input/output | address | a values                                     |
+# | `$a2`    | input/output | address | b values                                     |
+# | `$a3`    | input/output | address | c values                                     |
+# | `$v0`    | output       | integer | number of triplets                           |
+# | `$t0-9`  | temporary    | any     | for temporary storage                        |
+
+.globl triplets_with_sum
+
+triplets_with_sum:
+        jr $ra