RPN Calculator

An RPN calculator computes expressions written in Reverse Polish Notation.

An RPN expression or postfix expression is one of the following :

• a number X, in wich case the value of the expression is that of X,
• a sequence of form E1 E2 OP where E1 and E2 are RPN expressions and OP is an arithmetic operation.

Samples :

20 5 /        => 20/5 = 4
4 2 + 3 -     => (4+2)-3 = 3
3 5 8 * 7 + * => ((5*8)+7)*3 = 141

Add the SQRT operation :

9 SQRT => √9 = 3

Add the MAX operation :

5 3 4 2 9 1 MAX => MAX(5, 3, 4, 2, 9, 1) = 9
4 5 MAX 1 +     => MAX(4, 5) + 1 = 6

It’s important to have the discussion about absorbing property of MAX operator. With Reverse Polish Notation we must have a fixed number of operands by operator to avoid parentesis. For example : 4 5 MAX 1 2 MAX * could be replace in first step by 5 1 2 MAX * and in second step by 5 * but it’s not a valid expression. With a fixed number of operands by operator for example 2, 4 5 MAX 1 2 MAX * is a valid expression but 5 3 4 2 9 1 MAX not.