#lang racket
(require (planet dyoo/simply-scheme:2:2))

(define (parse expr)
  (parse-helper expr '() '()))

(define (parse-helper expr operators operands)
  (cond ((null? expr)
     (if (null? operators)
         (car operands)
         (handle-op '() operators operands)))
    ((number? (car expr))
     (parse-helper (cdr expr)
               operators
               (cons (make-node (car expr) '()) operands)))
    ((list? (car expr))
     (parse-helper (cdr expr)
               operators
               (cons (parse (car expr)) operands)))
    (else (if (or (null? operators)
              (> (precedence (car expr))
             (precedence (car operators))))
          (parse-helper (cdr expr)
                (cons (car expr) operators)
                operands)
          (handle-op expr operators operands)))))

(define (handle-op expr operators operands)
  (parse-helper expr
        (cdr operators)
        (cons (make-node (car operators)
                 (list (cadr operands) (car operands)))
              (cddr operands))))

(define (precedence oper)
  (if (member? oper '(+ -)) 1 2))

(define (compute tree)
  (if (number? (datum tree))
      (datum tree)
      ((function-named-by (datum tree))
         (compute (car (children tree)))
         (compute (cadr (children tree))))))

(define (function-named-by oper)
  (cond ((equal? oper '+) +)
    ((equal? oper '-) -)
    ((equal? oper '*) *)
    ((equal? oper '/) /)
    (else (error "no such operator as" oper))))