What's the fastest way to check if input String is a correct RPN expression?

Question

I came across a task which makes you check if a String passed as an argument to your method/function is a correct statement in the Reverse Polish Notation sense. It can contain lowercase alphabet letters, operation signs and integers. Is there any faster way to check it than to read every character separately and actually try to evaluate the whole expression?

Answer 1

You don't have to evaluate the whole expression but you do need to split it into tokens, and you have to know the valence of every operator (that is, how many operands it takes). For simplicity, let the valence of an operand be 0; then do the following:

Set stack_size to 0;
For Each token In expression:
    Set stack_size to stack_size + 1 - valence(token)
    If stack_size <= 0: Report failure
If stack_size == 1: Report success
Else              : Report failure

Examples using _ for unary minus.

expression:     3 4 + 1 * _
stack_size:   0 1 2 1 2 1 1 -> success

expression:     2 3 4 + 1 * _
stack_size:   0 1 2 3 2 3 2 2 -> failure (not 1 at the end)

expression:     2 3 + + 1 * _
stack_size:   0 1 2 1 0       -> failure (stack_size <= 0)