Polish Notation Converter

Standard arithmetic uses infix notation, where operators sit between operands (e.g., A + B). Polish notation, invented by mathematician Jan Łukasiewicz, places operators before their operands (prefix), while Reverse Polish Notation (RPN) places operators after them (postfix). The underlying algorithm utilizes a stack-based parsing method, commonly known as the Shunting-yard algorithm. Operators and operands are reordered based on strict operator precedence rules, allowing computers to evaluate expressions sequentially without requiring grouping symbols like parentheses.

Let us convert the standard infix expression 3 + 4 * 2 into Polish notation (prefix) and Reverse Polish notation (postfix). First, identify operator precedence: multiplication takes priority over addition. Step 1: Evaluate the higher-precedence operation 4 * 2. In prefix notation, this becomes * 4 2. Step 2: Incorporate the addition operation. The final prefix notation is + 3 * 4 2. For postfix notation, operands remain in their relative positions while operators follow their respective operands, resulting in 3 4 2 * +. Evaluating this from left to right yields 3 + (4 * 2) = 11.

When working with bracketed expressions, always resolve the innermost parentheses first to avoid precedence errors. Keep track of operator associativity; most standard arithmetic operations are left-associative, except for exponentiation. Double-check your operand counts—in a valid Polish notation sequence, the number of operands must always equal the number of operators plus one.