GATE 2024 CS2 Q.43: solution and answer

GATE 2024 · CS2Q.43 · 2 marks · MCQ

Consider the following expression: $x [i] = (p + r) * - s [i] + u / w$ . The following sequence shows the list of triples representing the given expression, with entries missing for triples (1), (3), and (6).

(0) (1) (2) (3) (4) (5) (6) (7) + uminus / + = p (1) u (3) (6) r w (4) (5)

Which one of the following options fills in the missing entries CORRECTLY?

GATE 2024 CS2 question 43: A table of eight triples (0) to (7), each with an operator and two operands. — Figure from the GATE 2024 CS2 paper. It is part of the question.

(A)
(1) =[] s i; (3) * (0) (2); (6) []= x i
(B)
(1) []= s i; (3) - (0) (2); (6) =[] x (5)
(C)
(1) =[] s i; (3) * (0) (2); (6) []= x (5)
(D)
(1) []= s i; (3) - (0) (2); (6) =[] x i

Answer and solution

ANSWER

Option (A): (1) =[] s i; (3) * (0) (2); (6) []= x i.

Official answer: ASource: Official answer key, GATE 2024 CS2 (IISc Bengaluru)

Apply precedence: unary minus binds tightest, then * and /, then +, then =. The right-hand side is $((p + r) * (- s [i])) + (u / w)$ , assigned to $x [i]$ .
Triple (0) is + p r, which gives $p + r$ . This is the left operand of *.
Triple (1) must fetch the value of $s [i]$ (an array element read, or rvalue). In triple notation an array read is =[] s i, so (1) is =[] s i. Triple (2), uminus (1), then negates it to give $- s [i]$ .
Triple (3) must combine the two operands of *, namely $p + r$ (triple (0)) and $- s [i]$ (triple (2)). So (3) is * (0) (2). It is a multiplication, not a subtraction, so options B and D are wrong.
Triples (4) and (5) compute $u / w$ and then add it to (3). This matches the printed table, which confirms (3) is the product.
Triple (7) is = (6) (5), an assignment of the value (5) to the location named by (6). So (6) must be the store target $x [i]$ . In triple notation an array store is []= x i, with operands $x$ and $i$ . Triple (7) then supplies the value, so (6) does not take (5) as an operand. This rules out options B and C, whose (6) uses (5) or =[].
Combining the three entries: (1) =[] s i, (3) * (0) (2), (6) []= x i. This is option A.

KEY IDEA

In triples, reading an array element is =[] a i. Storing into one is []= a i, followed by a separate = (that triple) value triple. The operator in (3) comes from the expression: * for the product of $(p + r)$ and $- s [i]$ .

WATCH OUT FOR

Swapping =[] (read) with []= (store), or giving the store triple the value (5) as its operand when the assignment triple (7) already carries it. Also reading the * between $(p + r)$ and $- s [i]$ as a minus sign because of the unary minus.

From the GATE 2024 CS2 paper. Every question of this paper · Download the full paper · All 2 Intermediate code questions, with notes