(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)))

;********************************************* my work begin from here

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

(define (successive-merge treeset);the treeset here must be in ascending order
  (if (null? (cddr treeset));test if treeset has only two elements
      (make-code-tree (car treeset) (cadr treeset))
      (successive-merge (merge-then-arrange treeset))))

(define (merge-then-arrange treeset)
  (addjoin-ascending (make-code-tree (car treeset) (cadr treeset)) (cddr treeset)))

(define (addjoin-ascending tree treeset)
  (cond ((null? treeset) (list tree))
        ((> (weight tree) (weight (car treeset)))
         (cons (car treeset) (addjoin-ascending tree (cdr treeset))))
        (else (cons tree treeset))))

(define (make-leaf-set pairs)
  (if (null? pairs)
      '()
      (let ((pair (car pairs)))
        (addjoin-ascending (make-leaf (car pair)    ; symbol
                               (cadr pair))  ; frequency
                           (make-leaf-set (cdr pairs))))))

;********************************************* for testing
(define sample-pairs '((A 4) (B 2) (C 2) (D 1)))
(generate-huffman-tree sample-pairs)