[sicp]huffman编码的实现 @ Scheme

#lang racket
(define (length items)
  (if (null? items)
      0
      (+ 1 (length (cdr items)))))

(define (element-of-set? x set)
  (cond ((null? set) false)
        ((equal? x (car set)) true)
        (else (element-of-set? x (cdr set)))))

(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 (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)))

(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))))

(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)
                               (cadr pair))
                    (make-leaf-set (cdr pairs))))))


(define (encode message tree)
  (if (null? message)
      ‘()
      (append (encode-symbol (car message) tree)
              (encode (cdr message) tree))))

(define (encode-symbol symbol tree)
  (if (element-of-set? symbol (symbols tree))
      (if (leaf? tree) 
          ‘()
          (let ((left-tree (left-branch tree))
                (right-tree (right-branch tree)))
            (if (or (null? left-tree) (not (element-of-set? symbol (symbols left-tree))))
                (cons 1 (encode-symbol symbol right-tree))
                (cons 0 (encode-symbol symbol left-tree)))))
      (error "symbol does not exist -- ENCODE-SYMBOL" symbol)))

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

(define (successive-merge set)
  (cond ((null? set) ‘())
        ((= 1 (length set)) (car set))
        (else (successive-merge 
               (adjoin-set (make-code-tree (car set) (cadr set))
                           (cddr set))))))

(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 ‘(A D A B B C A) sample-tree)
(define sample-message ‘(0 1 1 0 0 1 0 1 0 1 1 1 0))
(decode sample-message sample-tree)

(define hip-tree
  (generate-huffman-tree ‘((a 2) (boom 1) (Get 2) (job 2) (na 16) (Sha 3) (yip 9) (Wah 1))))

(display hip-tree)

(define hip-message 
  ‘(Get a job 
    Sha na na na na na na na na 
    Get a job
    Sha na na na na na na na na
    Wah yip yip yip yip yip yip yip yip yip 
    Sha boom))

(length (encode hip-message hip-tree))