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GATE CSE 2026 Session 2 Q45: Live variables at the exit of each block in a loop CFG

Question

Consider the control flow graph given below.

Control flow graph: ENTRY to B1 (a = b + c); B1 goes to B2 (d = a + e) and to B3 (e = a + f); B3 loops back to B1; B2 goes to B4 (g = d + e), which goes to EXIT
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Which one of the following options is the set of live variables at the exit point of each basic block?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: A (official GATE 2026 final answer key)

Concept used: Backward data flow: IN[B]=use[B]∪(OUT[B]−def[B])\text{IN}[B] = \text{use}[B] \cup (\text{OUT}[B] - \text{def}[B]), OUT[B]=⋃IN[succ]\text{OUT}[B] = \bigcup \text{IN}[\text{succ}].

First step: Start from OUT[B4] = ∅ and iterate the equations around the B1 → B3 → B1 loop until nothing changes.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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