Polish Notation Converter
Convert between infix, prefix (Polish), and postfix (Reverse Polish) notations
Polish Notation Operations
Use operators: +, -, *, /, ^, parentheses (), and numbers/variables
Example Conversions
Infix to Prefix Example
Infix: (3 + 4) * 5 - 2
Prefix: - * + 3 4 5 2
Process: Operators come before their operands
Infix to Postfix Example
Infix: (3 + 4) * 5 - 2
Postfix: 3 4 + 5 * 2 -
Process: Operators come after their operands
Evaluation Example
Postfix: 3 4 + 5 * 2 -
Step 1: 3 4 + → 7
Step 2: 7 5 * → 35
Step 3: 35 2 - → 33
Notation Types
Infix
a + b
Standard mathematical notation
Prefix (Polish)
+ a b
Operators before operands
Postfix (RPN)
a b +
Operators after operands
Operator Precedence
Higher numbers = higher precedence
Quick Tips
Polish notation eliminates the need for parentheses
Postfix is used in stack-based calculators
No precedence rules needed in Polish notations
Separate tokens with spaces in Polish expressions
Understanding Polish Notation
What is Polish Notation?
Polish notation, invented by logician Jan Łukasiewicz in 1924, is a mathematical notation that eliminates the need for parentheses and precedence rules. There are two main types: prefix (Polish) and postfix (Reverse Polish) notation.
Key Advantages
- •No parentheses needed
- •No operator precedence confusion
- •Efficient for computer evaluation
- •Unambiguous expression evaluation
Conversion Algorithms
Shunting Yard (Postfix)
Developed by Dijkstra in 1961, this algorithm converts infix to postfix notation using operator precedence and a stack data structure.
Stack-Based Evaluation
Both prefix and postfix expressions can be evaluated efficiently using a stack, making them ideal for computer implementations.
Applications
Used in programming language compilers, calculators (HP calculators), and computer science education for expression parsing.
Infix Notation
Standard mathematical notation
Requires parentheses and precedence rules
Prefix (Polish)
Operators before operands
Evaluated right to left
Postfix (RPN)
Operators after operands
Evaluated left to right