ITPEC FE Morning April 2022 Question 4

Reverse Polish Notation (RPN) — evaluate and match equivalent postfix expressions.

Given expression: 3 4 − 5 ×

Step-by-step evaluation:
- Push 3, push 4
- −: pop 4 and 3 → 3 − 4 = -1
- Push 5
- ×: pop 5 and -1 → -1 × 5 = -5

Result: -5

Checking each option:
- (a) 3 4 5 × − → 4 × 5 = 20, then 3 − 20 = -17
- (b) 4 5 − 3 × → 4 − 5 = -1, then -1 × 3 = -3
- (c) 5 3 4 − × → 3 − 4 = -1, then 5 × (-1) = -5 ✔
- (d) 5 4 3 − × → 4 − 3 = 1, then 5 × 1 = 5

Key rule: In RPN, operands are pushed onto a stack; when an operator appears, the top two values are popped. For non-commutative operators (−, ÷), the second-popped value is the left operand.

AI-generated — may contain errors