环路生成树算法（SICPHuffman编码树习题2.672.68）
#lang sicp
;辅助方法
(define (append list1 list2)
(if (null? list1)
list2
(cons (car list1) (append (cdr list1) list2))))
;huffman树的表示
;;叶节点
(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))
;;非叶节点
(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)))
;解码过程--以huffman树为依据将消息转换为表示的字符序列（解密）
(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))))
;编码过程--以huffman树为依据将字符序列转换为0/1二进制序列（加密）
(define (encode message tree)
(if (null? message)
'()
(append (encode-symbol (car message) tree)
(encode (cdr message) tree))))
(define (encode-symbol symbol tree)
(cond ((leaf? tree) '())
((symbol-in-tree? symbol (left-branch tree))
(cons 0 (encode-symbol symbol (left-branch tree))))
((symbol-in-tree? symbol (right-branch tree))
(cons 1 (encode-symbol symbol (right-branch tree))))
(else
(error "bad symbol -- ENCODE-SYMBOL" symbol))))
(define (symbol-in-tree? symbol tree)
(define (iter-symbols symbols)
(cond ((null? symbols) #f)
((eq? symbol (car symbols)) #t)
(else
(iter-symbols (cdr symbols)))))
(iter-symbols (symbols tree)))
;;根据字符频度表生成huffman树
(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)) ;weight
(make-leaf-set (cdr pairs))))))
(define (generate-huffman-tree pairs)
(successive-merge (make-leaf-set pairs)))
(define (successive-merge ordered_pairs)
(let ((len (length ordered_pairs)))
(cond ((> len 1)
(let ((first (car ordered_pairs))
(second (cadr ordered_pairs)))
(set! ordered_pairs
(adjoin-set (make-code-tree first second)
(cddr ordered_pairs))))
(successive-merge ordered_pairs))
((= len 1)
(car ordered_pairs)))))
;; 2.67
(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))
(decode sample-bits sample-tree)
;; 2.68
(define sample-message '(A D A B B C A))
(encode sample-message sample-tree)
;; 2.69
(define huffman-tree (generate-huffman-tree (list '(A 4) '(B 2) '(C 1) '(D 1))))
(encode sample-message huffman-tree)
(decode sample-bits huffman-tree)
;; 2.70
(define song-code-tree (generate-huffman-tree
(list '(A 2) '(NA 16) '(BOOM 1)
'(SHA 3) '(GET 2) '(YIP 9)
'(JOB 2) '(WAH 1))))
(length (encode '(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) song-code-tree)) ;; 共84个二进制位
;; 如采用定长编码8个频度的字符需要3个bit，歌曲中共包含3*2 9*2 10 2=36个字符，共需要36*3=108个二进制位，我来为大家科普一下关于环路生成树算法?下面希望有你要的答案，我们一起来看看吧!
环路生成树算法
#lang sicp
;辅助方法
(define (append list1 list2)
(if (null? list1)
list2
(cons (car list1) (append (cdr list1) list2))))
;huffman树的表示
;;叶节点
(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))
;;非叶节点
(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)))
;解码过程--以huffman树为依据将消息转换为表示的字符序列（解密）
(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))))
;编码过程--以huffman树为依据将字符序列转换为0/1二进制序列（加密）
(define (encode message tree)
(if (null? message)
'()
(append (encode-symbol (car message) tree)
(encode (cdr message) tree))))
(define (encode-symbol symbol tree)
(cond ((leaf? tree) '())
((symbol-in-tree? symbol (left-branch tree))
(cons 0 (encode-symbol symbol (left-branch tree))))
((symbol-in-tree? symbol (right-branch tree))
(cons 1 (encode-symbol symbol (right-branch tree))))
(else
(error "bad symbol -- ENCODE-SYMBOL" symbol))))
(define (symbol-in-tree? symbol tree)
(define (iter-symbols symbols)
(cond ((null? symbols) #f)
((eq? symbol (car symbols)) #t)
(else
(iter-symbols (cdr symbols)))))
(iter-symbols (symbols tree)))
;;根据字符频度表生成huffman树
(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)) ;weight
(make-leaf-set (cdr pairs))))))
(define (generate-huffman-tree pairs)
(successive-merge (make-leaf-set pairs)))
(define (successive-merge ordered_pairs)
(let ((len (length ordered_pairs)))
(cond ((> len 1)
(let ((first (car ordered_pairs))
(second (cadr ordered_pairs)))
(set! ordered_pairs
(adjoin-set (make-code-tree first second)
(cddr ordered_pairs))))
(successive-merge ordered_pairs))
((= len 1)
(car ordered_pairs)))))
;; 2.67
(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))
(decode sample-bits sample-tree)
;; 2.68
(define sample-message '(A D A B B C A))
(encode sample-message sample-tree)
;; 2.69
(define huffman-tree (generate-huffman-tree (list '(A 4) '(B 2) '(C 1) '(D 1))))
(encode sample-message huffman-tree)
(decode sample-bits huffman-tree)
;; 2.70
(define song-code-tree (generate-huffman-tree
(list '(A 2) '(NA 16) '(BOOM 1)
'(SHA 3) '(GET 2) '(YIP 9)
'(JOB 2) '(WAH 1))))
(length (encode '(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) song-code-tree)) ;; 共84个二进制位
;; 如采用定长编码8个频度的字符需要3个bit，歌曲中共包含3*2 9*2 10 2=36个字符，共需要36*3=108个二进制位
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