2.68

练习 2.68 过程encode以一个消息和一棵树为参数，产生出被编码消息所对应的二进制位的表：

 
(define (encode message tree)
  (if (null? message)
      '()
      (append 
       (encode-symbol (car message) tree)
       (encode (cdr message) tree)
       )
      )
  )
​x
 
#<undef>

其中的encode-symbol是需要你写的过程，它能根据给定的树产生出给定符号的二进制位表。你所设计的encode-symbol在遇到未出现在树中的符号时应报告错误。请用在练习2.67中得到的结果检查所实现的过程，工作中用同样一棵树，看看得到的结果是不是原来那个消息。

 
(define (encode-symbol char tree)
  (let 
    (
     (left (left-branch tree))
     (right (right-branch tree))
     )
    (if (leaf? left) 
        (if (eq? (symbol-leaf left) char) 
            (list '0)
            (if (leaf? right)
                (if (eq? (symbol-leaf right) char)
                    (list '1)
                    'error-not-found-in-tree
                    )
                (let
                  (
                   (right-res (encode-symbol char right))
                   )
                  (if 
                   (eq? 
                    right-res 
                    'error-not-found-in-tree
                    )
                   'error-not-found-in-tree
                   (append (list '1) (encode-symbol char right))
                   )
                  )
                )
            )
        (
         (let 
           (
            (left-res (encode-symbol char left))
            )
           (if (eq? (left-res 'error-not-found-in-tree))
               (encode-symbol char right)
               left-res
               )
           )
         )
        )
    )
  )
 
#<undef>

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)

 
(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)
     )
    )
   )
  )
​
​
(encode-symbol 'A sample-tree)
 
(0)

 
(encode (list 'A 'D 'A 'B 'B 'C 'A) sample-tree)
 
(0 1 1 0 0 1 0 1 0 1 1 1 0)

结果和 sample-message 一致！