Reverse Polish Notation

Reverse Polish notation (RPN) also called post-fixed notation, is a notation of arithmetic expressions where operands (numbers) are written before the operators (+, -, *, /) while avoiding the use of parentheses. The RPN is primarily adapted to a technical computer / electronic use, and has the characteristic of avoiding the use of parentheses.

The NPI notation displays operands before operators. This notation implies to write operands first and then the order of operations.

Example: a × (b + c) is written a b c + ×

The conversion algorithm into RPN is called the Shunting-yard method.

The notation has the advantage that it no longer uses parentheses, reducing errors, and is sometimes faster than a normal calculation. RPN is also used in some programming languages like Forth, but also in HP calculators and in some scientific computations where the gain up and computation time can be interesting.