SICP_2.40-2.43

#lang racket

;;;;;;;;;;;;;;;;;;;;;;;
(define (flatmap proc seq)
  (accumulate append nil (map proc seq)))

;;;;;;;;;;;;;;;;;2.40
(define nil '())

(define (accumulate op intial seq)
  (if (null? seq)
      intial
      (op (car seq)
          (accumulate op intial (cdr seq)))))

(define (enumerate-interval low high)
  (if (> low high)
      nil
      (cons low (enumerate-interval (+ low 1) high))))

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

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

(define (prime? n)
  (define (test number)
    (cond ((> (square number) n) #t)
          ((= (remainder n number) 0) #f)
          (else (test (+ number 1)))))
  (test 2))

(define (square x)
  (* x x))

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

;;;;;;;;test
(unique-pairs 5)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define (prime-sum-pairs n)
  (map make-pair-sum
       (filter prime-sum?
               (unique-pairs n))))

;;;;;;;;;test
(prime-sum-pairs 5)

;;;;;;;;;;;;;;;;;;;2.41 假设s等于7
(define (unique-triples n)
  (flatmap (lambda (i)
             (map (lambda (j)
                    (cons i j))
                  (unique-pairs (- i 1))))
           (enumerate-interval 1 n)))

(define (sum-equal? sum triple)
  (= sum (+ (car triple) (cadr triple) (caddr triple))))

;(define (sum-equal? sum triple)
; (= sum
;     (fold-right + 0 triple)))

(define (remove-triples-not-equal-to sum triple)
  (filter (lambda (current-triple)
            (sum-equal? sum current-triple))
          triple))

;;;;;;;;;;;;;;test
(remove-triples-not-equal-to 10 (unique-triples 13))

;;;;;;;;;;;;;;;;;;;;2.42
(define (queens board-size)
  (define (queen-cols k)
    (if (= k 0)
        (list empty-board)
        (filter
         (lambda (positions) (safe? k positions))
         (flatmap
         (lambda (rest-of-queens)
           (map (lambda (new-row)
                  (adjoin-position new-row k rest-of-queens))
                (enumerate-interval 1 board-size)))
        (queen-cols (- k 1))))))
  (queen-cols board-size))

(define (make-position row col)
  (cons row col))

(define (position-row position)
  (car position))

(define (position-col position)
  (cdr position))

(define empty-board null)

(define (adjoin-position row col positions)
  (append positions (list (make-position row col))))

(define (safe? col positions)
  (let ((kth-queen (list-ref positions (- col 1)))
    (other-queens (filter (lambda (q)
                            (not (= col (position-col q))))
                          positions)))
    (define (attacks? q1 q2)
      (or (= (position-row q1) (position-row q2))
          (= (abs (- (position-row q1) (position-row q2)))
             (abs (- (position-col q1) (position-col q2))))))
    (define (iter q board)
      (or (null? board)
          (and (not (attacks? q (car board)))
               (iter q (cdr board)))))
    (iter kth-queen other-queens)))

(queens 4)

2.42 尚未理解书上的queens函数 参考代码