ITPEC FE Morning April 2019 Question 3
ITPEC FE Morning April 2019 — Question 3 of 80
Postfix (Reverse Polish Notation) Evaluation — evaluate an arithmetic expression written in postfix notation using a stack.
To evaluate a postfix expression, scan left to right:
- Operand → push onto the stack
- Operator → pop two operands, apply the operator, push the result
For binary operators: the second popped value is the left operand, and the first popped is the right operand. This matters for non-commutative operations like − and ÷.
Given: A=4, B=3, C=5, D=6
Expression: A B 2 × + D B ÷ C × −
| Token | Action | Stack |
|---|---|---|
| A | push 4 | [4] |
| B | push 3 | [4, 3] |
| 2 | push 2 | [4, 3, 2] |
| × | 3 × 2 = 6 | [4, 6] |
| + | 4 + 6 = 10 | [10] |
| D | push 6 | [10, 6] |
| B | push 3 | [10, 6, 3] |
| ÷ | 6 ÷ 3 = 2 | [10, 2] |
| C | push 5 | [10, 2, 5] |
| × | 2 × 5 = 10 | [10, 10] |
| − | 10 − 10 = 0 | [0] |
Infix equivalent: (A + B × 2) − (D ÷ B × C) = (4 + 6) − (2 × 5) = 10 − 10 = 0
Why not others:
- (a) -3 — arithmetic error or incorrect operand ordering
- (c) 3 — arithmetic error
- (d) 40/3 — incorrect order of operands in division
Key rule: In postfix, scan left to right using a stack. For each operator, the second popped value is the left operand and the first popped is the right operand.
AI-generated — may contain errors
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