Postfix is a popular notation used in data structures and algorithms. It is also known as ‘Reverse Polish Notation’ (RPN).

In this notation, the operators are written after the operands. It eliminates the need for parentheses to indicate the order of operations.

## Why is Postfix Notation Important?

Postfix notation has several advantages over other notations, such as infix (traditional mathematical notation) and prefix (Polish) notations.

**Simplicity:**Postfix notation eliminates the need for parentheses and reduces ambiguity in mathematical expressions. It simplifies expression evaluation and makes it easier to implement algorithms.**Ease of Parsing:**The postfix notation can be easily parsed using a stack-based algorithm.This makes it efficient for computers to evaluate complex expressions.

**Evaluation Efficiency:**Postfix notation allows for efficient evaluation of mathematical expressions using a stack-based algorithm. It eliminates the need for recursive function calls or complex parsing techniques.

## How Does Postfix Notation Work?

In postfix notation, operators are placed after their operands. Let’s consider an example expression:

**3 4 + 5 ***

This expression can be evaluated as follows:

- We start from left to right, reading each element of the expression.
- If we encounter an operand (number), we push it onto the stack.
- If we encounter an operator, we pop the top two elements from the stack, perform the operation, and push the result back onto the stack.
- We repeat this process until we reach the end of the expression.
- The final result will be the top element of the stack.

Let’s evaluate the example expression step by step:

- Push 3 onto the stack.
- Push 4 onto the stack.
- Encounter ‘+’, so pop 4 and 3 from the stack, perform addition (4 + 3 = 7), and push the result (7) back onto the stack.
- Push 5 onto the stack.
- Encounter ‘*’, so pop 5 and 7 from the stack, perform multiplication (5 * 7 = 35), and push the result (35) back onto the stack.

The final result is ’35’ – which is the top element of the stack. Thus, ‘3 4 + 5 *’ evaluates to ’35’ in postfix notation.

## Applications of Postfix Notation

Postfix notation finds its applications in various areas:

__Evaluation of Mathematical Expressions:__Postfix notation simplifies expression evaluation. It is commonly used in calculators and computer programs that deal with complex mathematical calculations.__Compiler Design:__Postfix notation is used during lexical analysis and parsing stages of compiler design to evaluate arithmetic expressions efficiently.__Data Structures:__Postfix notation can be used to represent binary expression trees or parse expressions in data structures like stacks and queues.

### In Conclusion

The postfix notation provides a simple, efficient, and unambiguous way to represent mathematical expressions. Its use extends beyond basic arithmetic calculations to more complex areas like compiler design and data structures. Understanding postfix notation is a valuable skill for any programmer or computer science enthusiast.