;; Huffman Encoding

;; ADT for Huffman leaf

(define (make-leaf symbol weight)
  (list 'leaf symbol weight))

(define (leaf? obj)
  (and (pair? obj)
       (eq? (car obj) 'leaf)))

(define symbol-leaf cadr)
(define weight-leaf caddr)

(define (make-code-tree left right)
  (list left
        right
        (append (symbols left) (symbols right))
        (+ (weight left) (weight right))))

(define left-branch car)
(define right-branch cadr)
(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" 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 ex-pairs '((a 4) (b 2) (c 1) (d 1)))

(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-msg '(0 1 1 0 0 1 0 1 0 1 1 1 0))

(define (encode message tree)
  (if (null? message)
      '()
      (append (encode-symbol (car message) tree)
              (encode (cdr message) tree))))

(define (encode-symbol symbol tree)
  (define (iter branch code)
    (cond ((leaf? branch) (reverse! code))
          ((memq symbol (symbols (left-branch branch)))
           (iter (left-branch branch) (cons 0 code)))
          ((memq symbol (symbols (right-branch branch)))
           (iter (right-branch branch) (cons 1 code)))
          (else (error "symbol can't be encoded" symbol))))
  (iter tree '()))

(define (generate-huffman-tree pairs)
  (successive-merge (make-leaf-set pairs)))

(define (successive-merge leaf-set)
  (cond ((null? leaf-set) (error "bug in Huffman construction"))
        ((null? (cdr leaf-set)) (car leaf-set))
        (else 
         (successive-merge
          (adjoin-set (make-code-tree
                       (car leaf-set)
                       (cadr leaf-set))
                      (cddr leaf-set))))))

(define h1 (generate-huffman-tree ex-pairs))

(define m1 (encode '(a b c d c b a) h1))

(define d1 (decode m1 h1))

(define text1 "The algorithm for generating a Huffman tree is very simple. \
The idea is to arrange the tree so that the symbols with the lowest frequency \
appear farthest away from the root.  Begin with the set of leaf nodes, \
containing symbols and their frequencies, as determined by the initial data \
from which the code is to be constructed.  Now find tow leaves with the \
lowest weights and merge them to produce a node that has these two nodes as \
its left and right branches.  The weight of the new node is the sume of the \
two weights.  Remove the two leaves from the original set and replace them by \
this new node.  Now continue this process.  At each step, merge two nodes \
with the smallest weights, removing them from the set and replacing them with \
a node that has these two as its left and right branches.  The process stops \
when there is only one node left, which is the root of the entire tree.")

(define (symbolize str)
  (map (lambda (c) (string->symbol (string c)))
       (string->list str)))

(define (stats text)
  (let ((counts '()))
    (for-each (lambda (s)
                (let ((bind (assq s counts)))
                  (cond (bind (set-car! (cdr bind) (+ 1 (cadr bind))))
                        (else (set! counts (cons (list s 1) counts))))))
              (symbolize text))
    counts))