Add exercise 4.37

mceval/amb-pythagorean-triples.rkt

@@ -54,3 +54,19 @@
 (define (a-triple-with-sum-from n)
   (amb (a-triple-with-sum-between n (+ n 1))
        (a-triple-with-sum-from (+ n 1))))
+
+;; Exercise 4.37
+
+;; Alternative version from the book.  I think this will be more
+;; efficient because it only has to explore the values of k that are
+;; sums of the squares of i and j, rather than all integers from j up
+;; to high.
+(define (a-pythagorean-triple-between* low high)
+  (let ((i (an-integer-between low high))
+        (hsq (* high high)))
+    (let ((j (an-integer-between i high)))
+      (let ((ksq (+ (* i i) (* j j))))
+        (require (>= hsq ksq))
+        (let ((k (sqrt ksq)))
+          (require (integer? k))
+          (list i j k))))))