GATE CSE 2024 Session 1 Q48: Return value bounds of a loop computing x = x + x + y

Consider the following C function definition.

int f(int x, int y) {
  for (int i=0; i<y; i++) {
    x=x+x+y;
  }
  return x;
}

Which of the following statements is/are TRUE about the above function?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, D (official GATE 2024 final answer key)

Concept used: The update $x \to 2x + y$ repeated $y$ times gives a closed form.

First step: Show $x + y$ doubles each iteration, so the result is $2^y(x + y) - y$ .

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key