SICP_2.24-2.29

这一次的习题让我发现对cons和list的理解完全不是那么回事  参考资料

#lang racket

;;;;;;;;;;;;;;;2.24

(list 1 (list 2 (list 3 4)))

;;;;;;;;;;;;;;;2.25

;;;;;;;;;;;;（cdr （list 1 2）） 将产生list （car （list 1 2））
;;;;;;;;;;;;产生integer
;;;;;;;;;;;;(car '(1 . 2)) -> 1
;;;;;;;;;;;;(cdr '(1 . 2)) -> 2
;;;;;;;;;;;;注意序对和表的区别！！！
(car (cdr (car (cdr (cdr '(1 2 (5 7) 9))))))
(car (car '((7))))
(car (cdr (car (cdr (car (cdr (car (cdr (car (cdr (car (cdr
                               '(1 (2 (3 (4 (5 (6 7))))))
                               ))))))))))))

;;;;;;;;;;;;;;2.26
(define x (list 1 2 3))
(define y (list 4 5 6))

(append x y)
(cons x y)
(list x y)
;;;;;;;;;;;;2.27
(define (deep-reverse tree)
  (cond ((null? tree) '())
        ((not (pair? tree)) tree)
        (else (append (deep-reverse (cdr tree))
                      (list (deep-reverse (car tree)))))))

(deep-reverse '('(3 4) '(1 2)))
;;;;;;;;;;;;;;2.28
(define (fringe tree)
  (cond ((null? tree) '())
        ((not (pair? tree))  (list tree))
        (else (append (fringe (car tree))
                      (fringe (cdr tree))))))

(define lis1 (list (list 1 2) (list 3 4)))

;;test
(fringe lis1)
(fringe (list lis1 lis1))

;;;;;;;;;;;;;;2.29
(define (make-mobile left right)
  (list left right))

(define (make-branch length structure)
  (list length structure))

(define (left-branch mobile)
  (car mobile))
(define (right-branch mobile)
  (car (cdr mobile)))

(define (branch-length branch)
  (car branch))
(define (branch-structure branch)
  (car (cdr branch)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;思路不清晰时的写法
;(define (total-weight mobile)
 ; (cond ((null? mobile) 0)
  ;      ((not (pair? mobile)) mobile)
   ;     (else (+ (total-weight (branch-structure (left-branch mobile)))
    ;             (total-weight (branch-structure (right-branch mobile)))))))
;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define (total-weight2 mobile)
  (+ (branch-weight (left-branch mobile))
     (branch-weight (right-branch mobile))))

(define (branch-weight branch)
  (if (have-mobile? branch)
      (total-weight2 (branch-structure branch))
      (branch-structure branch)))

(define (have-mobile? branch)
  (pair? (branch-structure branch)))
;;test
(define mobile (make-mobile (make-branch 10 2)
                            (make-branch 10 (make-mobile (make-branch 10 20)
                                                      (make-branch 10 20)))))

(define mobile2 (make-mobile (make-branch 10 20)
                            (make-branch 11 20)))

;(total-weight2 mobile)
;(total-weight mobile)
;(total-weight2 mobile2)
;(total-weight mobile2)

;;;;;;;;;;torque
(define (branch-torque branch)
  (* (branch-length branch)
     (branch-weight branch)))

(define (branch-balanced? branch)
  (if (pair? (branch-structure branch))
      (balanced? (branch-structure branch))
      #t))

(define (balanced? mobile)
  (and (= (branch-torque (left-branch mobile))
          (branch-torque (right-branch mobile)))
       (branch-balanced? (left-branch mobile))
       (branch-balanced? (right-branch mobile))))
;;test
(define a (make-mobile (make-branch 2 2) (make-branch 2 2)))
(define b (make-mobile (make-branch 2 7) (make-branch 6 5)))

(balanced? a)
(balanced? b)

;;;;;;;;;;;;;;;;;(define (make-mobile left right)
;;;;;;;;;;;;;;;;;;        (cons left right))
;;;;;;;;;;;;;;;;;(define (right-branch mobile)
;;;;;;;;;;;;;;;;;;         (cdr branch))
;;;;;;;;;;;;;;;;;;记住list和cons list总是有个nil的