2.40.rkt

#lang sicp

(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 (accumulate f acc seq)
  (if (null? seq)
      acc
      (f (car seq)
         (accumulate f acc (cdr seq)))))
      


(define (append list1 list2)
        (if (null? list1) list2
            (cons (car list1) (append (cdr list1) list2))))


(define (double x) (* x 2))

(define (enumerate-interval low high)
  (if (> low high)
      nil
      (cons low (enumerate-interval (+ low 1) high))))
                            
(define (map proc items)
  (if (null? items)
      nil
      (cons (proc (car items))
            (map proc (cdr items)))))

(display (accumulate append
           nil
           (map (lambda (i)
                  (map (lambda (j) (list i j))
                       (enumerate-interval 1 (- i 1))))
                (enumerate-interval 1 5))))
(newline)

(display (map (lambda (i)
                  (map (lambda (j) (list i j))
                       (enumerate-interval 1 (- i 1))))
                (enumerate-interval 1 5)))

(define (flatmap proc seq)
  (accumulate append nil (map proc seq)))
  
(define (unique-pairs n)
  (flatmap
   (lambda (i)
     (map (lambda (j) (list i j))
          (enumerate-interval 1 (- i 1))))
   (enumerate-interval 1 n)))

(newline)

(display (unique-pairs 5))

(newline)

(define (make-pair-sum pair)
  (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))

(define (filter predicate sequence)
  (cond ((null? sequence) nil)
        ((predicate (car sequence))
         (cons (car sequence)
               (filter predicate (cdr sequence))))
        (else (filter predicate (cdr sequence)))))

(define (prime-sum? pair)
  (prime? (+ (car pair) (cadr pair))))

(define (prime-sum-pairs n)
  (map make-pair-sum
       (filter prime-sum? (unique-pairs n))))

(display (prime-sum-pairs 6))