solutions to 4.35, 4.36 and 4.37

[sicp.git] / src / sicp / ex4_36.rkt

diff --git a/src/sicp/ex4_36.rkt b/src/sicp/ex4_36.rkt
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+#lang racket
+
+(require "amb-eli.rkt")
+
+(define (an-integer-starting-from n)
+  (amb n (an-integer-starting-from (+ n 1))))
+
+(define (an-integer-between low high)
+  (assert (< low high))
+  (amb low (an-integer-between (+ low 1) high)))
+
+#|
+
+If we replace an-integer-between with an-integer-starting-from, then
+the k grows too high to invalid ranges and never stops. The way to accomplish
+correct values is to restrict i, j and k to valid ranges.
+
+|#
+
+;; using euclid's formula
+;; http://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple
+(define (pythagorean-triples)
+  (let [(n (an-integer-starting-from 1))]
+    (let [(m (an-integer-starting-from n))]
+      (assert (> m n))
+      (list (- (sqr m) (sqr n))
+            (* 2 m n)
+            (+ (sqr m) (sqr n))))))
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