ISRO CS 2023 Q.17: solution and answer

ISRO 2023 · CSQ.17 · 1 mark · MCQ

In Reverse Polish notation, expression A*B+C*D is written as

(A)
AB*CD*+
(B)
A*BCD*+
(C)
AB*CD+*
(D)
A*B*CD+

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

The postfix form is $A B * C D * +$ , option (a).

Official answer: ASource: ISRO's revised and final answer key of 16 February 2024

Reverse Polish (postfix) notation writes each operator after its two operands, so no brackets are needed.
Precedence: * binds tighter than +, so the expression is $(A * B) + (C * D)$ .
Convert the left product: $A * B \to A B *$ .
Convert the right product: $C * D \to C D *$ .
The + joins the two results, so it goes after both: $A B * C D * +$ , which is $A B * C D * +$ .
Check by evaluating the string with a stack: push A, push B, * gives $A * B$ ; push C, push D, * gives $C * D$ ; + adds the two results. This is the original expression.
Option (b) A*BCD*+ and option (d) A*B*CD+ are not valid postfix: each has a * right after the single operand A, with no second operand before it. Option (c) AB*CD+* evaluates to $(A * B) * (C + D)$ , a different expression.

KEY IDEA

Apply precedence first, then place every operator after its two operands: the two products are converted separately and the + goes last.

WATCH OUT FOR

Leaving an operator between operands, as in infix, or placing + before the second product so that it ends up applied to the wrong operands, as in $(A * B) * (C + D)$ .

From the ISRO CS 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 1 ISRO Linear structures question, with notes