SICP問題2.67

教科書で定義されているHuffman 符号化木の表現

(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)))
; 復号化手続き
(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))))
; 重みつき要素
(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))))))
; ((A 4) (B 2) (C 1) (D 1))のような記号と頻度の対のリストをとり
; Huffman アルゴリズムにより直ぐに合体される葉の、最初の順序づけられた
; 集合を構成する手続き
(define (make-leaf-set pairs)
  (if (null? pairs)
      '()
      (let ((pair (car pairs)))
	(adjoin-set (make-leaf (car pair)   ; 記号
			       (cadr pair)) ; 頻度
		    (make-leaf-set (cdr pairs))))))

教科書で定義されている符号化木と例題の通信文

(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))

で問題。decode 手続きを使った通信文の復号化

(decode sample-message sample-tree)
; (A D A B B C A)