with infix, or postfix, notation: without some form of delimiter, like (), to mark expression boundaries, you can not implement recursive operator precedence handling/parsing.
how would you parse this ?
1 + 5 * 10 / 4 - 23 * 4 / 5
compare to this:
(((1 + 5) * 10 / 4) - 23 * 4) / 5
fortunately for you :), a zillion other programmers have had to implement this: [
^]