Polish Notations

In the early 1920s, a Polish logician, Jan Lukasiewicz invented a special notation for prepositional logic that allows to eliminate all parenthesis from formulas.  The notation is called Polish Notation, which results in a less readable expression.  Depending upon the arrangement of operators and operands in an expression, Polish notation may be classified as:

• Infix Polish Notation
• Prefix Polish Notation
• Postfix Polish Notation

Infix Polish Notation:  In this notation, the operator comes between two operands.  For example: A+B, where A, B are operands and + is an operator.

Prefix Polish Notation:  In this notation, the operator comes before two operands.  For example: +AB.

Postfix Polish Notation:  In this notation, the operator comes after two operands.  For example: AB+.

Application of Stacks:

1. Parenthesis checker
2. Evaluation of Postfix expression
3. Evaluation of Prefix expression
4. Evaluation of Infix expression
5. Conversion from Infix to Postfix
6. Conversion from Infix to Prefix
7. Conversion from Postfix to Prefix
8. Conversion from Postfix to Infix
9. Conversion from Prefix to Postfix
10. Conversion from Prefix to Infix