**What Is Polish Notation and Reverse Polish Notation in Data Structure?**

Data structures are an essential part of computer science, and understanding different types of notations used in data structures is crucial for efficient programming. Two such notations widely used are Polish Notation (PN) and Reverse Polish Notation (RPN).

In this article, we will delve into the concepts of PN and RPN and explore their significance in data structure operations.

## Polish Notation (PN)

Polish Notation, also known as prefix notation, is a mathematical notation where operators are placed before their operands. In PN, the order of operations is determined solely by the position of operators.

This eliminates the need for parentheses to indicate precedence.

The basic syntax of PN is as follows:

__Operator Operand1 Operand2__

For example, consider the expression “3 + 4”. In PN, it would be written as “+ 3 4”.

Here, the operator “+” comes before its operands “3” and “4”. This notation allows for easy parsing and evaluation of mathematical expressions without any ambiguity.

## Reverse Polish Notation (RPN)

Reverse Polish Notation is an extension of Polish Notation that places operators after their operands. RPN, also known as postfix notation, eliminates the need for parentheses or operator precedence rules.

It uses a stack-based approach to evaluate expressions efficiently.

The basic syntax of RPN is as follows:

__Operand1 Operand2 Operator__

For example, let’s consider the expression “3 + 4” again. In RPN, it would be written as “3 4 +”.

Here, the operands “3” and “4” are placed before the operator “+”. To evaluate this expression using RPN, we start with the operands and apply the operator.

RPN simplifies expression evaluation by eliminating the need for parentheses and reducing ambiguity. It also allows for easy implementation of expression evaluation algorithms using stacks.

## Advantages of Polish Notations

Both PN and RPN have their advantages in data structure operations. Some key advantages are:

**No parentheses:**Polish notations eliminate the need for parentheses to indicate precedence, making expressions less complex and easier to read.**Unambiguous:**The order of operations in PN and RPN is clear, leaving no room for ambiguity during expression evaluation.**Efficient evaluation:**RPN uses a stack-based approach that allows for efficient evaluation of mathematical expressions.**Simpler parsing:**Both notations simplify parsing algorithms by eliminating the need for complex parsing rules or operator precedence tables.

## Conclusion

Polish Notation (PN) and Reverse Polish Notation (RPN) are mathematical notations that provide a simple and unambiguous way to represent mathematical expressions. These notations eliminate the need for parentheses or complex parsing rules, making them efficient for evaluating mathematical expressions in data structures.

Understanding these notations is essential for programmers who deal with expression evaluation algorithms.

So next time you come across an arithmetic expression, whether it’s in your code or elsewhere, you’ll have a better understanding of PN and RPN!