Ex-2.29

;a

(define (left-branch m)
  (car m))
(define (right-branch m)
  (cadr m))
(define (branch-length b)
  (car b))
(define (branch-structure b)
  (cadr b))

;b

;total weight of a mobile
(define (total-weight m)
  (+ (branch-total-weight (left-branch m))
     (branch-total-weight (right-branch m))))


;find total weight of a branch
(define (branch-total-weight b)
  (if (pair? (branch-structure b))
             (total-weight (branch-structure b))
             (branch-structure b)))

;test
(define b1 (make-branch 1 2))
(define b2 (make-branch 1 3))
(define m1  (make-mobile b1 b2))
(define b3 (make-branch 1 5))
(define b4 (make-branch 1 m1))
(define m (make-mobile b3 b4))
(total-weight m)
;Value: 10 

;c

(define (balanced? m)
  (let ((lb (left-branch m))
        (rb (right-branch m)))
    (and
     (branch-balanced? lb)
     (branch-balanced? rb)
     (=
      (* (branch-length lb) (branch-total-weight lb))
      (* (branch-length rb) (branch-total-weight rb))))))
;see if a branch has a mobile structure and its
;balanced, if it has weight then return true
(define (branch-balanced? b)
  (if (pair? (branch-structure b))
             (balanced? (branch-structure b))
             #t))

;test
(define b1 (make-branch 1 2))
(define b2 (make-branch 1 3))
(define m1  (make-mobile b1 b2))
(define b3 (make-branch 1 5))
(define b4 (make-branch 1 m1))
(define m (make-mobile b3 b4))
(balanced? m)
;Value: #f
(define b2 (make-branch 1 2))
(define m1  (make-mobile b1 b2))
(define b4 (make-branch 1 m1))
(define m (make-mobile b4 b4))
;value: #t 

;d
Since we abstracted out the details of how we select various component of mobile and branch, so only selectors need to change.

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