Polish Notation Converter

Polish notation is a way to write mathematical and logical expressions without relying on the usual placement of operators between values. In ordinary infix notation, an operator appears between its operands, as in A + B. Prefix notation places the operator first, producing + A B, while postfix notation places it last, producing A B +. Prefix form is often called Polish notation, and postfix form is known as Reverse Polish notation or RPN. Because an operator and its operands have an unambiguous order, prefix and postfix expressions generally do not need parentheses. This converter handles four common transformations: infix to prefix, infix to postfix, prefix to infix, and postfix to infix. For infix input, it recognizes identifiers, decimal numbers, parentheses, and the addition, subtraction, multiplication, division, and exponent operators. Standard precedence rules are applied: exponentiation is evaluated before multiplication and division, which are evaluated before addition and subtraction. Parentheses can explicitly change that order. Exponentiation is treated as right-associative, so a ^ b ^ c means a raised to the power of b raised to c. The infix conversions use the shunting-yard method to arrange tokens by precedence. A stack temporarily holds operators while values move directly to the output. Prefix output is then assembled from the resulting postfix sequence. Prefix-to-infix and postfix-to-infix conversions use a stack of partial expressions. Whenever an operator is encountered, the appropriate two operands are removed, combined, wrapped in parentheses, and returned to the stack. The final stack item is the complete infix expression. Token spacing matters for prefix and postfix input because spaces identify each operand and operator. Write * + A B C rather than *+ABC. Infix expressions may include or omit spaces because parentheses and operator characters separate the tokens. The converter preserves variable names and numeric values but adds spaces and parentheses to make the result easy to inspect. Notation conversion is useful when studying expression trees, compiler parsing, stack machines, calculators, and data structures. Postfix expressions can be evaluated from left to right with a simple stack, while prefix expressions can be processed similarly from right to left. Converting a familiar infix formula into either form makes operator precedence explicit and provides a practical way to check an expression-parsing exercise.