2.29

练习 2.29 一个二叉活动体由两个分支组成，一个是左分支，另一个是右分支。每个分支是一个具有确定长度的杆，上面或者吊着一个重量，或者吊着另一个二叉活动体。我们可以用复合数据对象表示这种二叉活动体，将它通过其两个分支构造起来（例如，使用list）：

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

分支可以从一个length（它应该是一个数）再加上一个structure构造出来，这个structure或者是一个数（表示一个简单重量），或者是另一个活动体：

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

a）请写出相应的选择函数left-branch和right-branch，它们分别返回活动体的两个分支。还有branch-length和branch-structure，它们返回一个分支上的成分。

b）用你的选择函数定义过程total-weight，它返回一个活动体的总重量。

c）一个活动体称为是平衡的，如果其左分支的力矩等于其右分支的力矩（也就是说，如果其左杆的长度乘以吊在杆上的重量，等于这个活动体右边的同样乘积），而且在其每个分支上吊着的子活动体也都平衡。请设计一个过程，它能检查一个二叉活动体是否平衡。

d）假定我们改变活动体的表示，采用下面构造方式：

(define (make-mobile left right)
    (cons left right))

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

你需要对自己的程序做多少修改，才能将它改为使用这种新表示？

a)

(define (compose f g) (lambda (x) (f (g x)))) 

(define left-branch car)
(define right-branch (compose car cdr)) 
(define branch-length car)
(define branch-structure (compose car cdr))

(define lb (make-branch 1 2))
(define rb (make-branch 2 4))

lb

rb

(define m (make-mobile lb rb))
m

(left-branch m)

(right-branch m)

b)

(define (total-weight m)
    (define (total-weight-of-mobile m)
        (define lb (left-branch m))
        (define rb (right-branch m))

        (define blb (branch-structure lb))
        (define brb (branch-structure rb))

        (+ 
            (total-weight blb)
            (total-weight brb)
        )
    )

    (if (pair? m) (total-weight-of-mobile m) m)
)

(= (total-weight m) 6)

c)

(define (balance? m) 
    (define lb (left-branch m))
    (define rb (right-branch m))
    (define blb (branch-structure lb))
    (define brb (branch-structure rb))

    (and
        (if (pair? blb) (balance? blb) #t)
        (if (pair? brb) (balance? brb) #t)
        (=
            (* (branch-length lb) (total-weight blb))
            (* (branch-length rb) (total-weight brb))
        )
    )
)

(balance? m)

d) 只需要修改一个选择函数，后面的高层函数完全不用修改！选择函数很好的完成了抽象屏障的作用

a) 改动： 可以省去 compose，直接调用 cdr

(define (make-mobile left right)
    (cons left right))

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


(define left-branch car)
(define right-branch cdr) 
(define branch-length car)
(define branch-structure cdr)

(define lb (make-branch 1 2))
(define rb (make-branch 2 4))

lb

rb

(define m (make-mobile lb rb))
m

(left-branch m)

(right-branch m)

b) 完全不用改

(define (total-weight-2 m)
  (define (total-weight-of-mobile m)
    (define lb (left-branch m))
    (define rb (right-branch m))

    (define blb (branch-structure lb))
    (define brb (branch-structure rb))

    (+ 
     (total-weight blb)
     (total-weight brb)
     )
    )

  (if (pair? m) (total-weight-of-mobile m) m)
  )

(= (total-weight-2 m) 6)

c) 完全不用改！

(define (balance-2? m) 
    (define lb (left-branch m))
    (define rb (right-branch m))
    (define blb (branch-structure lb))
    (define brb (branch-structure rb))

    (and
        (if (pair? blb) (balance? blb) #t)
        (if (pair? brb) (balance? brb) #t)
        (=
            (* (branch-length lb) (total-weight blb))
            (* (branch-length rb) (total-weight brb))
        )
    )
)

(balance-2? m)