Expression Evaluation (Cambridge International A-Level Computer Science)

Reverse Polish Notation (RPN)

What is RPN?

• Reverse Polish Notation (RPN) is a method of writing mathematical expressions where the operator comes after the operands

• This is also known as postfix notation

  • Infix: 3 + 4
  • RPN: 3 4 +

Why use RPN?

• No need for brackets: The order of operations is determined by position, not parentheses
• Easier for computers to evaluate using a stack
• Always unambiguous

How RPN works

• RPN uses a stack to evaluate expressions

1. Read from left to right
2. Push numbers onto the stack
3. When an operator is read:

• Pop the top two values from the stack
• Apply the operator
• Push the result back onto the stack

1. When the expression ends, the final result is at the top of the stack

Example: evaluate 3 4 + 2 ×

• Final result: 14

Example: convert this infix expression to RPN

• Split the expression into parts:
• Left-hand side:

(7 − 2 + 8)

• This becomes:

( (7 − 2) + 8 )

• Which in RPN is:

7 2 − 8 +

• Right-hand side:

(9 − 5)

• In RPN:

9 5 −

• Combine with the division
• In RPN, that becomes:

7 2 − 8 + 9 5 − ÷

Exam Hint RPN follows the evaluation order naturally, so there’s no need for brackets or precedence rules. Just:

• Work from inside brackets out
• Convert each sub-expression
• Add the operator after its operands

Summary