Pythagorean Triplets for Racket (#413)

Author: blakelewis

config.json

@@ -750,6 +750,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 6
+      },
+      {
+        "slug": "pythagorean-triplets",
+        "name": "pythagorean-triplets",
+        "uuid": "630a11f5-e640-4e4d-af01-30f3bbcf495c",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

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

@@ -0,0 +1,15 @@
+{
+  "authors": ["blakelewis"],
+  "files": {
+    "solution": [
+      "pythagorean-triplets.rkt"
+    ],
+    "test": [
+      "pythagorean-triplets-test.rkt"
+    ],
+    "example": [
+      ".meta/example.rkt"
+    ]
+  },
+  "blurb": "Find Pythagorean triplets with a given sum"
+}

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

@@ -0,0 +1,24 @@
+#lang racket
+
+(provide triplets-with-sum)
+
+(define (primitives pmax)
+  (for*/list
+    ([m (in-naturals 2)]
+     #:break (> (* 2 (* m (add1 m))) pmax)
+     [n (in-range (add1 (remainder m 2)) m 2)]
+     #:when (= 1 (gcd m n)))
+    (define a (- (* m m) (* n n)))
+    (define b (* 2 (* m n)))
+    (define c (+ (* m m) (* n n)))
+    (sort (list a b c) < )))
+
+(define (triplets-with-sum p)
+  (define (scale-up triple)
+     (define perimeter (for/sum ([t triple]) t))
+     (cond
+       [(zero? (remainder p perimeter))
+         (define k (quotient p perimeter))
+         (for/list ([t triple]) (* k t))]
+       [else #f]))
+   (sort (filter-map scale-up (primitives p)) < #:key car))

exercises/practice/pythagorean-triplets/.meta/example.rkt

@@ -0,0 +1,38 @@
+#lang racket/base
+
+(require "pythagorean-triplets.rkt")
+
+(module+ test
+
+  (require rackunit rackunit/text-ui)
+
+  (define suite
+    (test-suite
+      "Return Pythagorean triplets with given perimeter"
+
+      (test-equal? "triplets whose sum is 12"
+        (triplets-with-sum 12) '((3 4 5)))
+
+      (test-equal? "triplets whose sum is 108"
+        (triplets-with-sum 108) '((27 36 45)))
+
+      (test-equal? "triplets whose sum is 1000"
+        (triplets-with-sum 1000) '((200 375 425)))
+
+      (test-equal? "no matching triplets for 1001"
+        (triplets-with-sum 1001) '())
+
+      (test-equal? "returns all matching triplets"
+        (triplets-with-sum 90) '((9 40 41) (15 36 39)))
+
+      (test-equal? "several matching triplets"
+        (triplets-with-sum 840)
+        '((40 399 401) (56 390 394) (105 360 375) (120 350 370)
+          (140 336 364) (168 315 357) (210 280 350) (240 252 348)))
+
+      (test-equal? "triplets for large number"
+        (triplets-with-sum 30000)
+        '((1200 14375 14425) (1875 14000 14125) (5000 12000 13000)
+          (6000 11250 12750) (7500 10000 12500)))))
+
+  (run-tests suite))

exercises/practice/pythagorean-triplets/pythagorean-triplets-test.rkt

@@ -0,0 +1,6 @@
+#lang racket
+
+(provide triplets-with-sum)
+
+(define (triplets-with-sum p)
+  (error "Not implemented yet"))