weima learns to program

my attempt to do the exercises in sicp.

Monday, July 28, 2008

sicp exercise 2.67

;; Exercise 2.67.  Define an encoding tree and a sample message:

;; (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))

;; Use the decode procedure to decode the message, and give the result.

(define (make-leaf symbol weight)
(list 'leaf symbol weight))
(define (leaf? object)
(eq? (car object) 'leaf))

(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 (symbols tree)
(if (leaf? tree)
(list (symbol-leaf tree))
(define (weight tree)
(if (leaf? tree)
(weight-leaf 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 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))

(display sample-tree) (newline)

(display (decode sample-message sample-tree)) (newline)