Rpn

Rpn, short for Reverse Polish Notation, also known as postfix notation, is a mathematical notation in which every operator follows all of its operands. In RPN expressions, the order of evaluation is unambiguous and no parentheses are needed.

Evaluation of RPN uses a stack. Read tokens from left to right: when you encounter a number, push it onto the stack; when you encounter an operator, pop the appropriate number of operands, apply the operator, and push the result back on the stack. At the end, the stack contains the value of the expression.

Example: the expression "3 4 +" evaluates to 7. A more complex example, "5 1 2 + 4 * + 3 -", evaluates to 14. The steps involve pushing numbers, computing subexpressions with operators, and reducing to a final result.

RPN is commonly used in calculators and in stack-based programming languages. Hewlett-Packard’s scientific calculators popularized RPN in the late 20th century, and postfix notation is also used in languages such as PostScript and Forth, which execute expressions via a stack machine rather than a conventional infix parser.

Advantages of RPN include elimination of parentheses and straightforward, efficient parsing on stack-based hardware. Its primary limitations are reduced readability for humans accustomed to infix notation and the need for additional transformation when converting between infix expressions and RPN, typically using algorithms like the shunting-yard method.

See also Polish notation; postfix notation; stack machine.