Completed 2.41

2_40.sch

@@ -0,0 +1,89 @@
+(define (filter predicate sequence)
+  (cond ((null? sequence) '())
+        ((predicate (car sequence))
+         (cons (car sequence)
+               (filter predicate (cdr sequence))))
+        (else (filter predicate (cdr sequence)))))
+
+(define (accumulate op initial sequence)
+  (if (null? sequence)
+      initial
+      (op (car sequence)
+          (accumulate op initial (cdr sequence)))))
+
+(define (flatmap proc seq)
+  (accumulate append '() (map proc seq)))
+
+;(define (prime-sum? pair)
+;  (prime? (+ (car pair) (cadr pair))))
+
+(define (make-pair-sum pair)
+  (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))
+
+(define (smallest-divisor n)
+  (find-divisor n 2))
+
+(define (square x) (* x x))
+
+(define (find-divisor n test-divisor)
+  (cond ((> (square test-divisor) n) n)
+        ((divides? test-divisor n) test-divisor)
+        (else (find-divisor n (+ test-divisor 1)))))
+
+(define (divides? a b)
+  (= (remainder b a) 0))
+
+(define (prime? n)
+  (= n (smallest-divisor n)))
+
+
+
+
+(define (permutations s)
+  (if (null? s)                         ; empty set?
+      (list '())                        ; sequence containing empty set
+      (flatmap (lambda (x)
+                 (map (lambda (p) (cons x p))
+                      (permutations (remove x s))))
+               s)))
+
+(define (remove item sequence)
+  (filter (lambda (x) (not (= x item)))
+          sequence))
+
+(define (enumerate-interval low high)
+  (if (> low high)
+      '()
+      (cons low (enumerate-interval (+ low 1) high))))
+
+(define (unique-pairs n)
+  (flatmap
+    (lambda (i)
+      (map (lambda (j) (list i j))
+	   (enumerate-interval 1 (- i 1))))
+    (enumerate-interval 1 n)))
+
+(define (prime-sum-pairs n)
+  (map make-pair-sum
+       (filter prime-sum? (unique-pairs n))))
+
+
+; 2.41
+
+(define (ordered-triples n)
+  (flatmap
+    (lambda (i)
+      (flatmap 
+	(lambda (j)
+	  (map (lambda (k) (list i j k))
+	       (enumerate-interval 1 (- j 1))))
+	  (enumerate-interval 1 (- i 1))))
+    (enumerate-interval 1 n)))
+
+(define (sum l)
+  (if (null? l)
+      0
+      (+ (car l) (sum (cdr l)))))
+
+(define (triple-leq-n-sum-s n s)
+  (filter (lambda (x) (= (sum x) s)) (ordered-triples n)))