Suffix Notation (Reverse Polish Notation)

Overview

Suffix notation, commonly referred to as Reverse Polish Notation (RPN), is a mathematical notation where every operator follows all of its operands. This contrasts with the more familiar infix notation, where operators are placed between operands.

Contents

Overview Key Concepts How it Works Deep Dive Applications Challenges & Misconceptions FAQs Is RPN the same as postfix notation?What are the benefits of RPN?

Key Concepts

The core idea of RPN is to eliminate the need for parentheses and operator precedence rules during evaluation. Operands are pushed onto a stack, and when an operator is encountered, it operates on the top elements of the stack.

How it Works

Numbers (operands) are pushed onto a stack.
When an operator is encountered, the required number of operands are popped from the stack.
The operator is applied to the popped operands.
The result is pushed back onto the stack.

Deep Dive

Consider the expression 3 + 4 * 2 in infix notation. In RPN, this becomes 3 4 2 * +. The evaluation proceeds as follows:

Push 3. Stack: [3]
Push 4. Stack: [3, 4]
Push 2. Stack: [3, 4, 2]
Encounter ‘*’. Pop 2 and 4. Calculate 4 * 2 = 8. Push 8. Stack: [3, 8]
Encounter ‘+’. Pop 8 and 3. Calculate 3 + 8 = 11. Push 11. Stack: [11]

The final result, 11, is at the top of the stack.

Applications

RPN is notably used in:

Hewlett-Packard (HP) calculators: Many classic HP models utilized RPN for its efficiency and ease of use once learned.
Programming languages: Some interpreters and compilers use stack-based evaluation, which aligns well with RPN principles.
Computer science algorithms: Evaluating expressions and parsing are common areas where RPN concepts are applied.

Challenges & Misconceptions

The main challenge for new users is the unfamiliarity with the notation. It requires a shift in thinking from standard infix. A common misconception is that RPN is overly complex; however, its simplicity in parsing and evaluation is a significant advantage for machines.