In data structures, prefix and postfix notations are used to represent arithmetic expressions. These notations are also known as **Polish Notation** and **Reverse Polish Notation**, respectively. Both notations eliminate the need for parentheses and establish a clear order of evaluation for arithmetic operations.

## Prefix Notation

In prefix notation, also known as Polish notation, the operator appears before its operands. Each expression is enclosed in parentheses and consists of an operator followed by one or more operands.

For example, the prefix notation for the expression ‘3 + 4’ would be ‘+ 3 4’. In this case, the operator ‘+’ comes before the operands ‘3’ and ‘4’.

Prefix notation allows us to avoid ambiguity in evaluating arithmetic expressions. It ensures that each operation is performed on its respective operands without any confusion or ambiguity.

## Postfix Notation

In postfix notation, also known as Reverse Polish Notation (RPN), the operator appears after its operands. Similar to prefix notation, each expression is enclosed in parentheses.

For example, the postfix notation for the expression ‘3 + 4’ would be ‘3 4 +’. Here, the operator ‘+’ follows its operands ‘3’ and ‘4’, indicating that they should be added together.

The advantage of postfix notation is that it eliminates the need for parentheses altogether. The order of operations is determined solely by the position of operators and their corresponding operands.

## Differences between Prefix and Postfix

The main difference between prefix and postfix notations lies in their placement of operators with respect to their operands. In prefix notation, operators come before their operands, while in postfix notation, operators come after their operands.

Another significant difference is the order of evaluation. In prefix notation, the leftmost operator is evaluated first, followed by its operands. In postfix notation, the rightmost operator is evaluated first.

### Example of Prefix and Postfix Notations

Let’s consider the expression ‘2 * (3 + 4)’. We can represent this expression using both prefix and postfix notations:

#### Prefix Notation:

- ‘*’ represents multiplication
- ‘+’ represents addition
- The expression in prefix notation would be ‘* 2 + 3 4’

#### Postfix Notation:

- ‘*’ represents multiplication
- ‘+’ represents addition
- The expression in postfix notation would be ‘2 3 4 + *’

Both notations convey the same meaning; however, they differ in their arrangement of operators and operands.

## Conclusion

In conclusion, prefix and postfix notations are alternative ways to represent arithmetic expressions without parentheses. Prefix notation places operators before their operands, while postfix notation places operators after their operands. Both notations establish a clear order of evaluation for arithmetic operations, eliminating ambiguity and ensuring consistent computations.

By understanding these notations, developers can effectively analyze and evaluate arithmetic expressions in data structures.