GATE CS 2024 Set 1 — Question 48
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Programming & Data Structures → C Programming → Control Flow
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Question
Consider the following C function definition.Which of the following statements is/are TRUE about the above function?
int f(int x, int y) {
for (int i=0; i<y; i++) {
x=x+x+y;
}
return x;
}
Correct answer
(B) If the inputs are x=20, y=20, then the return value is greater than 2²⁰; (D) If the inputs are x=10, y=20, then the return value is greater than 2²⁰
Solution
The function updates the variable in a loop that iterates times. Let denote the value of after iterations, with being the initial input . The update rule in each iteration is:This is a linear recurrence relation. We can find the general term by observing the first few iterations:
- (A) and (C): For , the return value is .
- is much smaller than , so (A) is false.
- is greater than , so (C) is false.
- (B): For , the return value is . Since , (B) is true.
- (D): For , the return value is . Since , (D) is true.
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