Algorithm to evaluate prefix expression?

Question

I have a prefix expression that only has the 4 binary operators(+,-,*,/) .A straight forward way to evaluate such an expression is to convert it to a postfix expression and then evaluate that expression. But I am looking for an algorithm that does this directly without converting it to any other expression ?

Answer 1

Simple recursion:

Evaluate(input):
  Read a token from input.
  If the token is a value:
    Return the value of the token
  If the token is a binary operator:
    Let first_argument = Evaluate(input)
    Let second_argument = Evaluate(input)
    Return apply(operator, first_argument, second_argument)

Answer 2

Use a stack. Place your vars and operators and start popping each stack, one for operators and the other for varaiablss (the number of pops depending on arity).