Implement up to 2.41

ex-1_29-34.scm

@@ -1,21 +1,4 @@
-; utils
-(define (inc n) (+ n 1))
-(define (cube n) (* n n n))
-(define (square n) (* n n))
-(define (identity n) n)
-(define (even? n) (= (remainder n 2) 0))
-(define (odd? n) (= (remainder n 2) 1))
-(define (divides? a b) (= (remainder b a) 0))
-(define (gcd a b) (if (= b 0) a (gcd b (remainder a b))))
-
-; copied prime? from 1.21
-(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 (smallest-divisor n)
-  (find-divisor n 2))
-(define (prime? n) (if (= n 1) #f (= n (smallest-divisor n))))
+(load "util.scm")
 
 (display "ex-1.29") (newline)
 

ex-2_33-43.scm

@@ -107,7 +107,7 @@
 (display (fold-right list nil (list 1 2 3))) (newline) ; (1 (2 (3 ())
 (display (fold-left list nil (list 1 2 3))) (newline)  ; (() 1) 2) 3)
 
-(display "\nex-2.39\n")
+(display "\nex-2.39 - reverse via foldl and foldr\n")
 
 (define (reverse-l sequence)
   (fold-left (lambda (x y) (cons y x)) nil sequence))
@@ -119,5 +119,109 @@
 (display (reverse-r (list 1 2 3 4))) (newline)
 (display (reverse-l (list 1 2 3 4))) (newline)
 
-(display "\nex-2.40\n")
+(display "\nex-2.40 - prime pairs\n")
+
+(define (flatmap proc seq)
+  (accumulate append nil (map proc seq)))
+
+; Two versions for remove from me and the official one
+(define (remove x s)
+  (cond
+    ((null? s) s)
+    ((= x (car s)) (cdr s))
+    (else (cons (car s) (remove x (cdr s))))))
+
+(define (remove x s)
+  (accumulate (lambda (current rest)
+                (if (= current x) rest (cons current rest)))
+              nil s))
+
+(define (remove item sequence)
+  (filter (lambda (x) (not (= x item)))
+          sequence))
+
+(define (prime-sum? p) (prime? (+ (car p) (cadr p))))
+
+(define (prime-sum-pairs n)
+  (map make-pair-sum
+       (filter prime-sum?
+               (flatmap
+                (lambda (i)
+                  (map (lambda (j) (list i j))
+                       (enumerate-interval 1 (- i 1))))
+                (enumerate-interval 1 n)))))
+
+(define (permutations s)
+  (if (null? s)                    ; empty set?
+      (list nil)                   ; sequence containing empty set
+      (flatmap (lambda (x)
+                 (map (lambda (p) (cons x p))
+                      (permutations (remove x s))))
+               s)))
+
+(define (make-pair-sum p)
+  (list (car p) (cadr p) (+ (car p) (cadr p))))
+
+(display (permutations (list 1 2))) (newline)
+(display (prime-sum-pairs 3)) (newline)
+
+; Here starts the actual exercise
+(define (unique-pairs n)
+  (flatmap
+    (lambda (a) (map (lambda (b) (list a b)) (enumerate-interval 1 (- a 1))))
+    (enumerate-interval 1 n)))
+
+(display (unique-pairs 3)) (newline)
+
+(define (prime-sum-pairs n)
+  (map make-pair-sum
+       (filter prime-sum? (unique-pairs n))))
+
+(display (prime-sum-pairs 3)) (newline)
+
+
+(display "\nex-2.41 - unique triples\n")
+
+(define (unique-triples n)
+  (flatmap
+    (lambda (c)
+      (flatmap (lambda (b)
+                 (map (lambda (a) (list a b c))
+                  (enumerate-interval 1 (- b 1))))
+        (enumerate-interval 1 (- c 1))))
+      (enumerate-interval 1 n)))
+
+
+(define (add-lower-numbers xs)
+  (flatmap
+    (lambda (x)
+      (map (lambda (i) (cons i x))
+           (enumerate-interval 1 (- (car x) 1))))
+    xs))
+
+(define (unique-tuples n k)
+  (define (add-element tuples k)
+    (if (= k 0)
+      tuples
+      (add-element (add-lower-numbers tuples) (- k 1))))
+  (add-element (map list (enumerate-interval 1 n)) (- k 1)))
+
+(define (list-sum l)
+  (accumulate + 0 l))
+
+(define (unique-sum-triples n s)
+  (filter (lambda (t) (= (list-sum t) s)) (unique-triples n)))
+
+(display (unique-sum-triples 6 10)) (newline)
+
+(define (unique-sum-triples n s)
+  (filter (lambda (t) (= (list-sum t) s)) (unique-tuples n 3)))
+
+(display (unique-sum-triples 6 10)) (newline)
+
+(display "\nex-2.42\n")
+
+
+(display "\nex-2.43\n")
+
 

ex-2_44-52.scm

@@ -0,0 +1,21 @@
+(load "util.scm")
+
+(display "\nex-2.44\n")
+
+(display "\nex-2.45\n")
+
+(display "\nex-2.46\n")
+
+(display "\nex-2.47\n")
+
+(display "\nex-2.48\n")
+
+(display "\nex-2.49\n")
+
+(display "\nex-2.50\n")
+
+(display "\nex-2.51\n")
+
+(display "\nex-2.52\n")
+
+

util.scm

@@ -12,6 +12,25 @@
 
 (define (average a b) (/ (+ a b) 2.0))
 (define (id n) n)
+(define identity id)
 (define (inc n) (+ n 1))
 (define nil '())
+(define (divides? a b) (= (remainder b a) 0))
+(define (cube n) (* n n n))
+(define (even? n) (= (remainder n 2) 0))
+(define (odd? n) (= (remainder n 2) 1))
 
+; copied prime? from 1.21
+(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 (smallest-divisor n)
+  (find-divisor n 2))
+(define (prime? n) (if (= n 1) #f (= n (smallest-divisor n))))
+
+; https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-15.html
+(define (enumerate-interval low high)
+  (if (> low high)
+      nil
+      (cons low (enumerate-interval (+ low 1) high))))