#lang racket
(define (element-of-
set? x set
)(cond (
(null
?set
) #f)
((equal? x (car set
)) #t)
(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
(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-l 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-l (cdr bits) tree)
)(decode-l (cdr bits) next-branch)))
))(decode-l bits tree)
)(define (choose-branch bit branch)
(cond (
(= bit 0
)(left-branch branch))(
(= bit 1
)(right-branch branch))(
else
(error "bad bit -- chosse-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)
'()(encode (cdr message) tree)))
)(define (encode-symbol message tree)
(cond (
(leaf? tree)
null)(
(element-of-
set? message (symbols (left-branch tree)))
(cons 0
(encode-symbol message (left-branch tree)))
)((element-of-
set? message (symbols (right-branch tree)))
(cons 1
(encode-symbol message (right-branch tree)))
)(else
(error "bad bit -- chosse-branch" message)))
)(define (generate-huffman-tree pairs)
(successive-merge (make-leaf-
set pairs)))
(define (successive-merge set)(
if(=(length set)1
)(car set
)(successive-merge (adjoin-
set(make-code-tree (car set
)(cadr set))
(cddr set))
)))(define rock-pairs '((na
16)(yip9)
(sha3)
(a2)
(get2)
(job2)
(boom1)
(wah1)
))(define rock-tree (generate-huffman-tree rock-pairs)
)(define rock-code '(
geta
jobsha
nana
nana
nana
nana
geta
jobsha
nana
nana
nana
nana
wahyip
yipyip
yipyip
yipyip
yipyip
sha boom)
)(encode rock-code rock-tree)
'(11
1111
1001
1110
1110
0000
0000
1111
1110
0111
1011
1000
0000
0011
0101
0101
0101
0101
0101
0111
0110
11)
如果使用定長編碼表示8個符號，需要定長編碼位3位，一共是36個符號，定長編碼需要108個二進位制位可以表示。
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