Question

Consider the following C function definition: \begin{verbatim} int f(int x, int y) { for (int i = 0; i<y; i++) { x = x + x + y; } return x; } \end{verbatim} Which of the following statements is/are TRUE about the above function?

• A. If the inputs are \( x = 20, y = 10 \), then the return value is greater than \( 2^{20} \)
• B. If the inputs are \( x = 20, y = 20 \), then the return value is greater than \( 2^{20} \)
• C. If the inputs are \( x = 20, y = 10 \), then the return value is less than \( 2^{10} \)
• D. If the inputs are \( x = 10, y = 20 \), then the return value is greater than \( 2^{20} \)

Hint:

Exponential growth in iterative processes leads to extremely large values quickly. Always analyze the iteration logic carefully for such functions.

Answer 1

The Correct Option is B

Step 1: Understand the function.
The function iterates \( y \) times. In each iteration, the value of \( x \) is updated as \( x = x + x + y \), which simplifies to \( x = 2x + y \). Starting with the initial value of \( x \), the function exponentially increases \( x \) over \( y \) iterations. Step 2: Analyze the cases.
For \( x = 20, y = 10 \): After 10 iterations, the value of \( x \) becomes significantly large, and it exceeds \( 2^{10} = 1024 \). Thus, the return value is greater than \( 2^{10} \).
For \( x = 20, y = 20 \): After 20 iterations, \( x \) grows even more exponentially and far exceeds \( 2^{20} \). Thus, the return value is greater than \( 2^{20} \).
For \( x = 10, y = 20 \):
Similarly, with \( x = 10 \) and \( y = 20 \), the function results in \( x \) exceeding \( 2^{20} \).
\( x = 20, y = 10 \): The return value is never less than \( 2^{10} \), so this case is invalid. Final Answer: \[ \boxed{(2), (4)} \]