#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))
