ITPEC FE Morning October 2022 Question 4

Reverse Polish Notation (RPN) — evaluate a postfix arithmetic expression using a stack.

Expression: 9 2 1 + - 3 ×

Step-by-step using a stack:

• •Push 9, 2, 1
• •+ → pop 2 and 1 → 2 + 1 = 3 → push 3
• •- → pop 9 and 3 → 9 - 3 = 6 → push 6
• •Push 3
• •× → pop 6 and 3 → 6 × 3 = 18 → push 18

Result: 18 → answer is (d)

Why not others:
- (a) 0 — incorrect order of operations
- (b) 4 — likely confused subtraction operand order
- (c) 10 — incorrect grouping of operators

Key rule: In RPN, each operator pops the top two stack values; the second-to-top is the left operand, the top is the right operand. For - and ÷, operand order matters.

AI-generated — may contain errors