Reverse Polish Notation (RPN)

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Last updated 12:35 PM on 2/23/25
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8 Terms

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Reverse Polish Notation (RPN)
An unambiguous method for representing an expression left to right without needing rules of precedence or brackets.
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Advantages of RPN
No brackets or precedence of operators needed, simpler to evaluate, no backtracking in evaluation.
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How does the RPN evaluation work with a stack?
Values are pushed into the stack as they are read; operators pop the last two values, perform the operation, and push the result back.
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Example of converting regular notation to RPN: (a–b)∗(a+c)/7
Becomes ab−ac+∗7/ in RPN.
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Operator evaluation in RPN
Operators appear in the order required for computation, allowing evaluation from left to right.
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Read direction of RPN expression
RPN expression is read left to right.
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What happens when an operator is read in RPN?
The last two values in the stack are popped, the operator is applied, and the result is pushed back.
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Final RPN conversion example for (a/b)∗4−(a+b)
Becomes ab/4∗ab+− in RPN.