In data structure, infix and prefix are two different ways to represent arithmetic expressions. These notations are used to determine the order of operations in an expression. In this article, we will explore what infix and prefix notations are, their differences, and how they are used in data structure.

## Infix Notation

Infix notation is the most commonly used notation for representing arithmetic expressions. In this notation, the operators are placed between the operands. For example, the expression “2 + 3” is written as “2 + 3” in infix notation.

One of the key features of infix notation is that it follows the standard mathematical conventions for order of operations. This means that multiplication and division are performed before addition and subtraction. If there are multiple operators of the same precedence level, they are evaluated from left to right.

### Example:

Consider the following expression:

**5 + 3 * 2 – 4 / 2**

In infix notation, this expression would be evaluated as follows:

- Multiplication:
__3 * 2__= 6 - Division:
__4 / 2__= 2 - Addition:
__5 + 6__= 11 - Subtraction:
__11 – 2__= 9

## Prefix Notation

In contrast to infix notation, prefix notation places operators before their operands. This makes it a more concise way of representing arithmetic expressions. For example, the expression “2 + 3” is written as “+ 2 3” in prefix notation.

Prefix notation is also known as Polish notation, named after the Polish mathematician Jan Ćukasiewicz who introduced it in the 1920s.

### Example:

Consider the same expression as before:

**5 + 3 * 2 – 4 / 2**

In prefix notation, this expression would be written as:

**– + 5 * 3 2 / 4 2**

## Differences Between Infix and Prefix Notations

There are several key differences between infix and prefix notations:

**Operator Placement:**In infix notation, operators are placed between operands, while in prefix notation, operators are placed before operands.**Parentheses:**In infix notation, parentheses are used to specify the order of operations. In prefix notation, the order of operations is determined by the position of operators.**Evaluation Order:**In infix notation, operators with higher precedence are evaluated before operators with lower precedence. In prefix notation, operators are evaluated from left to right.

## Usage in Data Structure

In data structure algorithms like expression evaluation or conversion, both infix and prefix notations have their importance.

Infix notation is commonly used by humans because it follows the standard mathematical conventions that we are familiar with. However, for computers to evaluate arithmetic expressions efficiently, they need a more structured representation like prefix notation.

Prefix notation allows us to evaluate arithmetic expressions using stacks in an efficient manner. It eliminates the need for parentheses and reduces ambiguity in the order of operations. Furthermore, converting an expression from infix to prefix can simplify the evaluation process for computers.

Overall, infix and prefix notations play a crucial role in data structure algorithms that involve arithmetic expressions. Understanding their differences and applications can help us design more efficient algorithms and simplify complex computations.

So, whether you are solving a mathematical problem or implementing an algorithm, having a good understanding of infix and prefix notations will undoubtedly prove beneficial.