ITPEC FE Morning April 2022 Question 4

5 3 4 − × — the given expression is (3 − 4) × 5 = −5, and this one computes 5 × (3 − 4), the same value.

Evaluate RPN with a stack: push operands, and on an operator pop two values, the first popped being the right operand.

• •3 4 − 5 ×: 3 − 4 = −1, then −1 × 5 = −5
• •5 3 4 − ×: push 5, then 3 − 4 = −1, then 5 × (−1) = −5

Multiplication is commutative, so the factor 5 may come first, but the subtraction must stay 3 − 4 in that order.

Answer (c)

Why not others:

• •(a) 3 4 5 × − — this is 3 − 4 × 5 = −17; the multiplication happens before the subtraction
• •(b) 4 5 − 3 × — this is (4 − 5) × 3 = −3, different operands for both operators
• •(d) 5 4 3 − × — this is 5 × (4 − 3) = 5; the subtraction's operands are reversed

Key rule: Commutative operators (+, ×) let you swap their operands in RPN; for − and ÷ the operand order must be kept.

Basic Theory · AI-written, may contain errors