GATE CS 2026 Set 1 — Question 61
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Programming & Data Structures → C Programming → Functions & Recursion
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Question
Consider the recursive functions represented by the following code segment:The smallest positive integer for which
int bar(int n){
if (n == 1) return 0;
else return 1 + bar(n/2);
}
int foo(int n){
if (n == 1) return 1;
else return 1 + foo(bar(n));
}
foo(n) returns 5 is ______. (answer in integer)Note: Ignore syntax errors (if any) in the function.Correct answer
65536 to 65536
Solution
The function
bar(n) calculates the floor of the base-2 logarithm of , i.e., .The function foo(n) is defined recursively as:- for
1.
2.Let .
3.Let .
4.Let .
Since , we need .To find the smallest , we find the smallest possible value at each step:- Smallest such that .
- Smallest such that .
- Smallest such that .
- Smallest such that .
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