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Reverse Polish Notation is an alternative way of writing mathematical expressions, where the operator goes after the operands.

Diagram 1 shows how the expression 9 + 10 can be converted to Reverse Polish Notation.

Diagram 1

But why use Reverse Polish Notation? Consider the infix expression (3 + 7) / (6 - 4). In RPN, the parentheses are never required, as the order of operations can be inferred by the order of operators in the expression: 3 7 + 6 4 - /.

Also, Reverse Polish Notation can be easily evaluated by stack-based interpreters.

Diagram 2 shows how the RPN expression 3 7 + 6 4 - / could be evaluated by a stack-based interpreter.

Diagram 2

Examples of interpreters that use RPN include Postscript, the Java Virtual Machine (to run bytecode), and Thunno 2.

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Convert the RPN expression 7 4 - 15 8 + * to infix and evaluate the result.

(7 - 4) * (15 + 8) (answer is 69).

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