# 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.