Note: Do not use spaces in expression. A+B/C or 4+5/3
not A + B / C or 4 + 5 / 3

Updated (26 Feb 2023)

Infix -> Postfix & Prefix

This is a simple infix to prefix or postfix Converter.

Enter the Infix expression below in box and press Convert

Type the Expression below without space
format 1: 2+4/5*(5-3)^5^4
format 2: A+B/C*(D-A)^F^H
(NO SPACE)

Postfix Table Prefix Table

Evaluate >

Postfix : | Prefix :

By Raj

Sr. no.	Expression	Stack	Postfix

Algorithm used

Postfix

Step 1: Add ")" to the end of the infix expression
Step 2: Push "(" onto the stack
Step 3: Repeat until each character in the infix notation is scanned
- 3.1: IF a "(" is encountered, push it on the stack
- 3.2: IF an operand ( whether a digit or a character) is encountered, add it postfix expression.
- 3.3: IF a ")" is encountered, then
  a. Repeatedly pop from stack and add it to the postfix expression until a "(" is encountered.
  b. Discard the "(". That is, remove the(from stack and do not add it to the postfix expression
- 3.4: IF an operator O is encountered, then
  a. Repeatedly pop from stack and add each operator ( popped from the stack) to the postfix expression which has equal or higher precedence than O
  b. Push the operator O to the stack.
[END OF IF]
Step 4: Repeatedly pop from the stack and add it to the postfix expression until the stack is empty
Step 5: EXIT

Prefix

Step 1: Reverse the infix string. Note that while reversing the string you must interchange left and right parentheses.
Step 2: Obtain the postfix expression of the expression obtained from Step 1 using the above given postfix algorithm with slight change in Step 3.4

IF an operator O is encountered, then
a. Repeatedly pop from stack and add each operator ( popped from the stack) to the postfix expression which has ~~equal or~~ higher precedence than O
Step 3: Reverse the postfix expression to get the prefix expression

Understanding the Infix to Postfix & Prefix Converter

Our Infix to Postfix & Prefix Converter is a powerful tool designed to transform mathematical expressions between different notations. This converter is particularly useful for students, programmers, and anyone working with expression parsing or compiler design.

What are Infix, Postfix, and Prefix Notations?

Infix Notation: This is the standard way we write mathematical expressions, with operators placed between operands. Example: A + B * C
Postfix Notation (Reverse Polish Notation): In this notation, operators follow their operands. Example: A B C * +
Prefix Notation (Polish Notation): Here, operators precede their operands. Example: + A * B C

How to Use the Converter

Enter your infix expression in the input box. Remember not to use spaces between characters.
Valid formats include:
- Numeric expressions: 2+4/5*(5-3)^5^4
- Algebraic expressions: A+B/C*(D-A)^F^H
Click the "Convert" button to see the postfix and prefix equivalents.
Review the conversion tables to understand the step-by-step process.

Features of Our Converter

Dual Conversion: Provides both postfix and prefix notations simultaneously.
Step-by-Step Breakdown: Displays the conversion process in detail, helping users understand the algorithm.
Support for Complex Expressions: Handles nested parentheses and multiple operators with different precedences.
Evaluation Option: Includes a link to evaluate the converted expressions.

Why Use Different Notations?

While infix notation is more readable for humans, postfix and prefix notations have several advantages:

They eliminate the need for parentheses and operator precedence rules.
They are easier for computers to parse and evaluate.
They are used in many programming languages and calculators.

Applications

This converter is valuable for:

Students learning about expression parsing and notation conversion.
Programmers implementing expression evaluators or compilers.
Anyone looking to understand or work with different mathematical notations.

By using this tool and studying the conversion process, you can gain a deeper understanding of how mathematical expressions are structured and processed in different notations. This knowledge is fundamental in various areas of computer science and mathematics.