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))

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)