2.67

练习 2.67 请定义一棵编码树和一个样例消息：

 
(define sample-tree
  (make-code-tree 
   (make-leaf 'A 4)
   (make-code-tree 
    (make-leaf 'B 2)
    (make-code-tree
     (make-leaf 'D 1)
     (make-leaf 'C 1)
     )
    )
   )
  )
​
(define sample-message '(0 1 1 0 0 1 0 1 0 1 1 1 0))
​x
 
Error: execute: unbound symbol: "make-leaf" []true

然后用过程 decode 完成该消息的编码，给出编码的结果。

decode 的代码如下：

 
(define (decode bits tree)
  (define (decode-1 bits current-branch)
    (if (null? bits)
        '()
        (let 
          (
           (next-branch
            (choose-branch 
             (car bits)
             current-branch
             )
            )
           )
​
          (if (leaf? next-branch)
              (cons 
               (symbol-leaf next-branch) 
               (decode-1 (cdr bits) tree)
               )
              (decode-1 (cdr bits) next-branch)
              )
          )
        )
    )
​
  (decode-1 bits tree)
  )
​
(define (left-branch tree) (car tree))
(define (right-branch tree) (cadr tree))
​
(define (choose-branch bit branch)
  (cond 
   ((= bit 0) (left-branch branch))
   ((= bit 1) (right-branch branch))
   (else
    (error "bad bit -- CHOOSE-BRANCH" bit)
    )
   )
  )
​
(define (make-leaf symbol weight)
  (list 'leaf symbol weight)
  )
​
(define (leaf? object) (eq? (car object) 'leaf))
​
(define (symbol-leaf x) (cadr x))
(define (weight-leaf x) (caddr x))
​
​
(define (make-code-tree left right)
  (list 
   left
   right
   (append (symbols left) (symbols right))
   (+ (weight left) (weight right))
   )
  )
​
(define (symbols tree)
  (if (leaf? tree)
      (list (symbol-leaf tree))
      (caddr tree))
  )
​
(define (weight tree)
  (if 
   (leaf? tree)
   (weight-leaf tree)
   (cadddr tree)
   )
  )
​
(define sample-tree
  (make-code-tree 
   (make-leaf 'A 4)
   (make-code-tree 
    (make-leaf 'B 2)
    (make-code-tree
     (make-leaf 'D 1)
     (make-leaf 'C 1)
     )
    )
   )
  )
​
(define sample-message '(0 1 1 0 0 1 0 1 0 1 1 1 0))
​
(decode sample-message sample-tree)
 
('A 'D 'A 'B 'B 'C 'A)