GATE CSE 2011 | Question: 49

Question

Consider the following recursive C function that takes two arguments.

unsigned int foo(unsigned int n, unsigned int r) {
    if (n>0) return ((n%r) + foo(n/r, r));
    else return 0;
}

What is the return value of the function $\text{foo}$ when it is called as $\text{foo(513, 2)}$?

• A. $9$
• B. $8$
• C. $5$
• D. $2$

Comments

same Q appeared in ISRO 2020

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Can anyone confirm time complexity will be $\large O(log_{2}n)$

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ASNR1010 Base must be r.

Answer 1

The function returns the sum of digits in a binary representation of the given number

so $1+0+0+0+0+0+0+0+0+1 = 2$

Correct Answer: $D$

Comments

if you simulate this program with different values of n and r, notice that this function foo(n,r) gives the sum of digits of n(when it is converted to base r).

Like if n=513, r=14 then $(513)_{10}=(289)_{14}$ and 2+8+9=19 and this is the output of the program.

Answer 2

Final return value is 2 So option d