**What Is Postfix Infix in Data Structure?**

Data structures play a crucial role in computer science and programming. They are the building blocks that allow us to efficiently store and retrieve data.

One such data structure is the postfix infix notation. Let’s dive deeper into what it entails and how it works.

## Postfix Notation

Postfix notation, also known as Reverse Polish Notation (RPN), is a mathematical notation in which every operator follows all of its operands. This means that there are no parentheses required to indicate the order of operations.

In postfix notation, expressions are evaluated from left to right. To calculate an expression in postfix notation, we use a stack-based algorithm.

## Infix Notation

In contrast, infix notation is the standard mathematical notation we are most familiar with. In infix notation, operators are placed between their operands, and parentheses are used to indicate the order of operations.

While infix notation is easy for humans to read and write, it can be challenging for computers to evaluate directly. To overcome this challenge, we can convert an infix expression into a postfix expression using an algorithm called the Shunting Yard Algorithm.

## Converting Infix to Postfix

The Shunting Yard Algorithm allows us to convert an infix expression into a postfix expression. This algorithm uses stacks to achieve the conversion.

The basic idea behind this algorithm is as follows:

- Create two stacks: one for operators and one for output
- Scan the infix expression from left to right
- If an operand is encountered, add it to the output stack
- If an operator is encountered:
- If the operator stack is empty or contains an opening parenthesis, push the operator onto the stack
- If the operator has higher precedence than the top of the operator stack, push it onto the stack
- If the operator has lower or equal precedence than the top of the operator stack, pop operators from the stack and add them to the output until a lower precedence operator is encountered or an opening parenthesis is reached. Then, push the current operator onto the stack.
- If a closing parenthesis is encountered, pop operators from the stack and add them to the output until an opening parenthesis is reached. Discard both parentheses.
- Repeat steps 3-7 until all tokens have been scanned
- Pop any remaining operators from the stack and add them to the output

Once we have successfully converted an infix expression to postfix notation, we can evaluate it using a postfix evaluation algorithm.

## Evaluating Postfix Notation

Evaluating a postfix expression involves iterating through each token from left to right. If an operand is encountered, it is pushed onto a stack. If an operator is encountered, two operands are popped from the stack, and then their result after applying that operation is pushed back onto the stack.

This process continues until all tokens have been processed. At this point, only one value should remain on the stack, which represents the final result of evaluating that postfix expression.

## Conclusion

In summary, postfix infix notation provides a more efficient way for computers to evaluate mathematical expressions compared to traditional infix notation. By converting infix expressions to postfix notation and then evaluating them using stacks, we can simplify complex arithmetic operations in programming languages and other computing applications.

Understanding postfix infix notation is essential for computer scientists and programmers alike, as it allows us to build more efficient algorithms and data structures that deal with mathematical expressions.