GATE CS 2019 Q26 — Asymptotic Worst Case Time and Space Complexity

To understand the behavior of the function, let us trace the execution of convert(n) with a positive integer, say $n = 5$:

1. convert(5):
   • Since $5 < 0$ is false, the else block is executed.
   • It calls convert(5/2), which is convert(2).
2. convert(2):
   • Since $2 < 0$ is false, it calls convert(2/2), which is convert(1).
3. convert(1):
   • Since $1 < 0$ is false, it calls convert(1/2), which is convert(0).
4. convert(0):
   • Since $0 < 0$ is false, it calls convert(0/2), which is convert(0).
5. convert(0):
   • This again calls convert(0), leading to infinite recursion.

Because the recursive call convert(n/2) is placed before the print statement printf("%d", n%2), the program must wait for the recursive call to complete before it can print anything.

Since the recursion gets stuck in an infinite loop at $n = 0$ and never terminates, the control never reaches any of the printf statements. Thus, the function will not print anything and will not terminate (practically, it will eventually result in a stack overflow error).