学步园

　　最近在看SICP书，第二章有一节关于霍夫曼编码的，把书上的部分代码，再加上我自己做的练习，整理出来一些代码。

　　包括编码，解码，生成编码树。

　　传说中的Scheme哦:(

　　

(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))

;; makers
(define (make-code-tree left right)
  (list left
        right
        (append (symbols left) (symbols right))
        (+ (weight left) (weight right))))
        
;; selectors
(define (left-branch tree) (car tree))
(define (right-branch tree) (cadr tree))
(define (symbols tree)
  (if (leaf? tree)
      (list (symbol-leaf tree))
      (caddr tree)))
(define (weight tree)
  (if (leaf? tree)
      (weight-leaf tree)
      (cadddr tree)))
      
;; decoding
(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 (choose-branch bit branch)
  (cond ((= bit 0) (left-branch branch))
        ((= bit 1) (right-branch branch))
        (else (error "bad bit -- CHOOSE-BRANCH" bit))))

;; encoding
(define (encode message tree)
  (if (null? message)
      '()
      (append (encode-symbol (car message) tree)
              (encode (cdr message) tree))))

(define (member? x ls) (and (member x ls) #t))
(define (encode-symbol s tree) ; 2.68
  (cond ((null? tree) '())
        ((leaf? tree) '())
        ((member? s (symbols (left-branch tree)))
         (cons '0 (encode-symbol s (left-branch tree))))
        ((member? s (symbols (right-branch tree)))
         (cons '1 (encode-symbol s (right-branch tree))))
        (else (error "bad symbol -- encode-sympol" s))))

;; generate tree
(define (adjoin-set x set)
  (cond ((null? set) (list x))
        ((< (weight x) (weight (car set))) (cons x set))
        (else (cons (car set)
                    (adjoin-set x (cdr set))))))

(define (make-leaf-set pairs)
  (if (null? pairs)
      '()
      (let ((pair (car pairs)))
        (adjoin-set (make-leaf (car pair)    ; symbol
                               (cadr pair))  ; frequency
                    (make-leaf-set (cdr pairs))))))

(define (generate-huffman-tree pairs)
  (successive-merge (make-leaf-set pairs)))

(define (successive-merge sub-trees) ; 2.69
  (if (= (length sub-trees) 1)
      (car sub-trees)
      (let ((new-node (make-code-tree (car sub-trees)
                                      (cadr sub-trees))))
        (successive-merge (adjoin-set new-node (cddr sub-trees))))))
                                 
; for test
(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-bits '(0 1 1 0 0 1 0 1 0 1 1 1 0))
(equal? sample-bits
        (encode (decode sample-bits sample-tree) sample-tree))
(equal? sample-tree  
        (generate-huffman-tree '((A 4) (B 2) (C 1) (D 1))))

博客园不支持scheme代码，只能贴plaintext了:P