-
Notifications
You must be signed in to change notification settings - Fork 0
/
2_40.scm
50 lines (40 loc) · 1.33 KB
/
2_40.scm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
(define (enumerate from to)
(if (> from to)
'()
(cons from (enumerate (+ from 1) to))))
(define (permutations s)
(if (null? s) ; empty set?
(list '()) ; sequence containing empty set
(map (lambda (x)
(map (lambda (p) (cons x p))
(permutations (remove (lambda (a) (= a x)) s))))
s)))
(define (flatmap proc seq)
(accumulate append '() (map proc seq)))
(define (accumulate op initial sequence)
(if (null? sequence)
initial
(op (car sequence)
(accumulate op initial (cdr sequence)))))
(define (unique-pairs n)
(flatmap (lambda (i)
(map (lambda (j) (cons j (cons i '())))
(enumerate 1 (- i 1))))
(enumerate 1 n)))
(define (make-pair-sum pair)
(list (car pair) (cadr pair) (+ (car pair) (cadr pair))))
(define (prime-sum? pair)
(prime? (+ (car pair) (cadr pair))))
(define (smallest-divisor n)
(find-divisor n 2))
(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 (prime-sum-pairs n)
(map make-pair-sum
(filter prime-sum? (unique-pairs n))))