Infix to Prefix Converter
Prefix Notation:
None
Examples to Try:
- A+B → + A B
- (A+B)*C → * + A B C
- A*(B+C)/D → / * A + B C D
- A+B*C-D → - + A * B C D
Free Online Infix to Prefix Notation Converter
Convert infix expressions to prefix (Polish) notation instantly using our powerful online tool. Designed for computer science students, developers, and anyone learning data structures and expression parsing. This tool handles all basic arithmetic operators, brackets, and complex expressions with ease — making it perfect for academic use and exam preparation.
🧠 What is Infix and Prefix Notation?
Infix Notation is the common way of writing mathematical expressions, where the operator is placed between the operands.
Example:
A + B
Prefix Notation, also known as Polish Notation, places the operator before the operands.
Example:
+ A B
So, the infix expression (A + B) * C becomes the prefix expression * + A B C.
🔄 Why Use Infix to Prefix Conversion?
In computer science, especially in the fields of expression parsing, compilers, and stack-based algorithms, converting infix expressions to prefix notation is crucial. Prefix expressions eliminate the need for parentheses and follow a strict operator precedence, making them easier to evaluate programmatically using stacks.
🧮 Steps to Convert Infix to Prefix Notation
1. Reverse the infix expression (e.g., A + B * C becomes C * B + A)
2. Swap parentheses (change ( to ) and vice versa)
3. Convert the reversed expression to postfix using the standard infix-to-postfix conversion algorithm
4. Reverse the result to get the final prefix expression
Example Conversion:
Infix: (A + B) * (C - D)
Reversed: (D - C) * (B + A)
Swap brackets: (D - C) * (B + A)
Postfix of reversed: D C - B A + *
Final Prefix: * + A B - C D
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✅ Key Points to Remember
- Prefix notation does not use parentheses; operator precedence is inherently maintained by the order.
- Always use stack-based logic when writing code for conversion.
- Operator Precedence: ^ > *// > +/-
- Associativity matters, especially for operators like ^ which is right-associative.
- Always reverse the expression and handle brackets carefully during conversion.
🚀 Features of This Online Converter Tool
- 100% Free and Instant conversion
- Supports *+, -, , /, ^ operators and parentheses
- Mobile-friendly and easy-to-use interface
- Suitable for students, teachers, developers, and competitive programmers
- Helpful in learning compiler design, stack algorithms, and notation systems
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