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In computer science, the shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation.It can produce either a postfix notation string, also known as reverse Polish notation (RPN), or an abstract syntax tree (AST). [1]
Video: Keys pressed for calculating eight times six on a HP-32SII (employing RPN) from 1991. Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands.
In infix notation, unlike in prefix or postfix notations, parentheses surrounding groups of operands and operators are necessary to indicate the intended order in which operations are to be performed. In the absence of parentheses, certain precedence rules determine the order of operations.
In computer science, an operator-precedence parser is a bottom-up parser that interprets an operator-precedence grammar.For example, most calculators use operator-precedence parsers to convert from the human-readable infix notation relying on order of operations to a format that is optimized for evaluation such as Reverse Polish notation (RPN).
Multiplication normally has higher precedence than addition, [1] for example, so 3+4×5 = 3+(4×5) ≠ (3+4)×5. In terms of operator position, an operator may be prefix, postfix, or infix. A prefix operator immediately precedes its operand, as in −x. A postfix operator immediately succeeds its
The rank of an operation is called its precedence, and an operation with a higher precedence is performed before operations with lower precedence. Calculators generally perform operations with the same precedence from left to right, [ 1 ] but some programming languages and calculators adopt different conventions.
Immediate-execution calculators are based on a mixture of infix and postfix notation: binary operations are done as infix, but unary operations are postfix. Because operators are applied one-at-a-time, the user must work out which operator key to use at each stage, and this can lead to problems.
The position of the operator with respect to its operands may be prefix, infix or postfix (suffix [1]), and the syntax of an expression involving an operator depends on its arity (number of operands), precedence, and (if applicable), associativity.