Algorithms | Recursion | Question 8

Predict the output of following program 

C

#include <stdio.h>
int f(int n)
{
    if(n <= 1)
        return 1;
    if(n%2 == 0)
        return f(n/2);
    return f(n/2) + f(n/2+1);
}


int main()
{
    printf(\"%d\", f(11));
    return 0;
}

(A)

Stack Overflow

(B)

3

(C)

4

(D)

5

Answer: (D)
Explanation:

On successive recursion F(11) will be decomposed into F(5) + F(6) -> F(2) + F(3) + F(3) -> F(1) + 2 * [F(1) + F(2)] -> 1 + 2 * [1 + F(1)] -> 1 + 2 * (1 + 1) -> 5. 

Hence, option D is the correct answer.

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