Reverse Polish Notation - Explanation

Explanation

In reverse Polish notation the operators follow their operands; for instance, to add 3 and 4, one would write "3 4 +" rather than "3 + 4". If there are multiple operations, the operator is given immediately after its second operand; so the expression written "3 − 4 + 5" in conventional infix notation would be written "3 4 − 5 +" in RPN: first subtract 4 from 3, then add 5 to that. An advantage of RPN is that it obviates the need for parentheses that are required by infix. While "3 − 4 * 5" can also be written "3 − (4 * 5)", that means something quite different from "(3 − 4) * 5". In postfix, the former could be written "3 4 5 * −", which unambiguously means "3 (4 5 *) −" which reduces to "3 20 −"; the latter could be written "3 4 - 5 *" (or 5 3 4 - *, if you wish to keep similar formatting), which unambiguously means "(3 4 -) 5 *".

Despite the name, reverse Polish notation is not exactly the reverse of Polish notation, for the operands of non-commutative operations are still written in the conventional order (e.g. "/ 6 3" in Polish notation and "6 3 /" in reverse Polish both evaluating to 2, whereas "3 6 /" in reverse Polish notation would evaluate to ½).