Prefix and postfix notations are useful alternatives to the more common infix notation for writing and evaluating mathematical expressions. Here are some key reasons why prefix and postfix notations are needed:
Eliminate the need for parentheses: Infix notation requires parentheses to specify the order of operations, which can make expressions longer and harder to read. Prefix and postfix notations eliminate the need for parentheses by always evaluating operators in a fixed order[1][2].
Easier to evaluate using algorithms: Prefix and postfix expressions can be evaluated more efficiently using stack-based algorithms that scan the expression from left-to-right or right-to-left. This makes them well-suited for implementation in computer programs[2][3].
Unambiguous order of operations: In infix notation, operator precedence rules and parentheses are used to determine the order of operations. Prefix and postfix notations eliminate ambiguity by always evaluating operators in a fixed order based on their position relative to the operands[1][2].
Useful in reverse Polish notation calculators: Postfix notation is commo...
