(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)    ; symbol
                             (cadr pair))  ; frequency
                  (make-leaf-set (cdr pairs))))))

 symbol
 frequency
(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)))
                  (make-leaf-set (cdr pairs))))))
