Reverse Polish Notation (RPN), also known as postfix notation, is a mathematical notation system used to represent and evaluate mathematical expressions. In RPN, the operators are placed after their operands, making it different from the traditional infix notation.
In this notation, each operator follows all of its operands. For example, the expression "3 + 4" written in RPN would be presented as "3 4 +". This means that the operator "+" is applied to the operands "3" and "4". The resulting value is then placed on the stack, which is a data structure used for evaluating RPN expressions.
RPN eliminates the need for parentheses and explicit operator precedence rules by employing a stack-based evaluation method. As the expression is scanned from left to right, each number encountered is placed on the stack. When an operator is encountered, it is applied to the topmost operands on the stack, and the result is placed back on the stack.
The advantage of using RPN is its simplicity and unambiguous representation of mathematical expressions. It eliminates the need for parentheses and allows for easy implementation in computer programs and calculators. Furthermore, RPN requires fewer computational steps, as it does not have an intermediate evaluation order.
This notation was popularized by Polish logician Jan Łukasiewicz, but the term "reverse Polish notation" was coined by Charles Hamblin in the 1950s. It has since gained widespread use in calculators, computer languages, and mathematical software.
