#| BEGIN (Write your solution here) |#
; Code from the book
(define (deriv-preorder exp var) (cond ((number? exp) 0) ((variable? exp) (if (same-variable? exp var) 1 0)) ((sum? exp) (make-sum (deriv-preorder (addend exp) var) (deriv-preorder (augend exp) var)))
((product? exp) (make-sum (make-product (multiplier exp) (deriv-preorder (multiplicand exp) var))
(make-product (deriv-preorder (multiplier exp) var) (multiplicand exp))))
(else (error "unknown expression type: DERIV" exp))))
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2) (and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (sum? x) (and (pair? x) (eq? (car x) '+)))
(define (addend s) (cadr s))
(define (product? x) (and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (=number? exp num) (and (number? exp) (= exp num)))
(define (make-product m1 m2) (cond ((or (=number? m1 0) (=number? m2 0)) 0) ((=number? m1 1) m2) ((=number? m2 1) m1) ((and (number? m1) (number? m2)) (* m1 m2)) (else (list '* m1 m2))))
(define (make-sum a1 a2) (cond ((=number? a1 0) a2) ((=number? a2 0) a1) ((and (number? a1) (number? a2)) (+ a1 a2))
(else (list '+ a1 a2))))
(define (augend s) (caddr s))
(define (multiplicand p) (caddr p))

; My code
(define (deriv exp var)
    (let ((preorder (to-preorder exp)))
        ; (display 'preorder:)
        ; (display preorder)
        ; (newline)
        (deriv-preorder preorder var)
    )
)

(define (preorder? exp)
    (cond
        ((null? exp) #t)
        ((not (pair? exp)) #t)
        ((eq? (car exp) '+) #t)
        ((eq? (car exp) '*) #t)
        (else #f)
    )
)

(define (to-preorder exp)
    (cond
        ((preorder? exp) exp)
        ((= (length exp) 1) (to-preorder (car exp)))
        (else
            (let ((term1 (car exp)) (op (cadr exp)) (term2 (cddr exp)))
                (cond
                    ((eq? op '+) (make-sum (to-preorder term1) (to-preorder term2)))
                    ((eq? op '*)
                        (cond
                            ((= (length term2) 1) (make-product (to-preorder term1) (to-preorder term2)))
                            (else (to-preorder (cons (make-product (to-preorder term1) (car term2)) (cdr term2))))
                        )
                    )
                )
            )
        )
    )
)
#| END |#