GATE CS 2024 Set 1 Q.48: Data Types, Operators and Control Flow

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?

If the inputs are x=20, y=10, then the return value is greater than $2^{20}$

If the inputs are x=20, y=20, then the return value is greater than $2^{20}$

If the inputs are x=20, y=10, then the return value is less than $2^{10}$

If the inputs are x=10, y=20, then the return value is greater than $2^{20}$

Official answer and solution

Solution

Find the closed-form value of x after y iterations of x = 2*x + y and compare with $2^{10}$ and $2^{20}$ .

In each iteration of the loop (i = 0 to y - 1), x is updated to $2x + y$ . Starting from initial value $x_0$ , after $y$ iterations:

x_{\text{final}} = x_0 \cdot 2^y + y(2^y - 1) = (x_0 + y)2^y - y

For $x_0 = 20, y = 10$ : $x_{\text{final}} = 30 \cdot 2^{10} - 10$ Since $2^{10} < 30 \cdot 2^{10} - 10 < 32 \cdot 2^{10} = 2^{15} < 2^{20}$ , both (A) and (C) are FALSE.
For $x_0 = 20, y = 20$ : $x_{\text{final}} = 40 \cdot 2^{20} - 20 > 2^{20} \implies \textbf{(B) is TRUE}.$
For $x_0 = 10, y = 20$ : $x_{\text{final}} = 30 \cdot 2^{20} - 20 > 2^{20} \implies \textbf{(D) is TRUE}.$

Final answer

Options (B), (D)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

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