What Is Reverse Polish Notation (RPN)?

Understanding Reverse Polish Notation (RPN)

Welcome to the “Definitions” section of our blog! In this post, we are going to explore the concept of Reverse Polish Notation (RPN). If you’ve ever come across this term and wondered what it actually means, you’re in the right place. Let’s dive right in!

Reverse Polish Notation, also known as postfix notation, is a mathematical notation system that is often associated with calculators and computer programming. Unlike the more conventional infix notation, where operators are placed between the operands (e.g., 2 + 2), RPN places the operators after the operands.

So, how does RPN work? Let’s break it down:

1. Start with a stack (a pile of numbers) and an empty result buffer.
2. Read the input from left to right, one token (number or operator) at a time.
3. If the token is a number, push it onto the stack.
4. If the token is an operator, pop the top two numbers from the stack, perform the operation, and push the result back onto the stack.
5. Repeat steps 3 and 4 until all the tokens have been processed.
6. The final result will be the last number remaining in the stack.

Here’s a simple example to illustrate RPN in action:

Consider the expression: 2 3 + 4 *

Using RPN, we would interpret this as:

1. Push 2 onto the stack.
2. Push 3 onto the stack.
3. Encounter the + operator. Pop 3 and 2 from the stack, add them, and push the result (5) onto the stack.
4. Push 4 onto the stack.
5. Encounter the * operator. Pop 4 and 5 from the stack, multiply them, and push the result (20) onto the stack.

The final result, 20, remains as the only number in the stack.

Now you might be wondering, why would we use RPN instead of the traditional infix notation? Well, there are a few advantages:

• RPN eliminates the need for parentheses as the operator precedence is automatically determined by the order of operations.
• It allows for easier implementation in computer programs and calculators.
• RPN notation can be evaluated from left to right without any need for backtracking.

Now that you understand the basics of Reverse Polish Notation (RPN), you’ll be able to appreciate its usefulness in various applications. Whether you’re exploring computer programming, working with calculators, or simply expanding your mathematical knowledge, RPN is a valuable concept to understand.

That wraps up our exploration of RPN. We hope this article has provided you with a clear understanding of what Reverse Polish Notation is and how it works. Be sure to check out our other “Definitions” blog posts for more informative content!