The infix notation is a widely used method of writing mathematical expressions. In the context of data structures, infix refers to the way operators are placed between operands to form an expression. In this article, we will explore what infix is and how it is used in data structures.

**What is Infix Notation?**

Infix notation is a method of representing mathematical expressions where operators are placed between operands. It is the most common way we write arithmetic expressions, such as __2 + 3__. The infix notation makes it easier for humans to read and understand mathematical expressions compared to other notations like prefix or postfix.

**Using Infix in Data Structures**

In data structures, infix notation is often used when dealing with arithmetic expressions and evaluating them. For example, consider the infix expression __(5 + 2) * 3__. To evaluate this expression, we need to follow a set of rules called operator precedence.

### Operator Precedence

Operator precedence determines the order in which operations are performed within an expression. For example, in the expression __(5 + 2) * 3__, the addition operation inside the parentheses should be performed before the multiplication operation outside the parentheses.

**Parentheses:**Operations inside parentheses are performed first.**Multiplication and Division:**These operations are performed before addition and subtraction.**Addition and Subtraction:**These operations are performed last.

**Evaluating Infix Expressions**

To evaluate an infix expression, we can use a technique called infix evaluation. This involves converting the infix expression into either postfix or prefix notation using algorithms like Shunting Yard or Reverse Polish Notation (RPN). Once converted, we can then evaluate the expression using stack-based algorithms.

**Converting Infix to Postfix**

One common approach to converting infix expressions to postfix is by using the Shunting Yard algorithm. This algorithm scans the infix expression from left to right and uses a stack to keep track of operators.

### Steps for Converting Infix to Postfix:

- Initialize an empty stack and an empty output queue.
- Scan the infix expression from left to right.
- If the scanned element is an operand, add it to the output queue.
- If the scanned element is an operator, compare its precedence with the operators in the stack:
- If the stack is empty or contains a left parenthesis on top, push the operator onto the stack.
- If the precedence of the scanned operator is greater than that of the operator at the top of the stack, push it onto the stack.
- If none of these conditions apply, pop operators from the stack and add them to the output queue until an operator with lower precedence or a left parenthesis is encountered. Then push the scanned operator onto the stack.
- If a left parenthesis is encountered, push it onto the stack.
- If a right parenthesis is encountered, pop operators from the stack and add them to the output queue until a matching left parenthesis is encountered. Discard both parentheses.

**Conclusion**

Infix notation plays a crucial role in representing arithmetic expressions in data structures. Understanding infix evaluation and conversion techniques allows us to evaluate mathematical expressions efficiently. By converting infix expressions into postfix or prefix notations, we can simplify their evaluation process using algorithms like Shunting Yard or Reverse Polish Notation (RPN).

**References:**

[1] – https://en.wikipedia.org/wiki/Infix_notation

[2] – https://en.org/wiki/Shunting-yard_algorithm