Official PYQ · 2010Q35Algorithm Design: Dynamic ProgrammingMCQ1 mark

GATE CS 2010 Q35 — Algorithm Design: Dynamic Programming

What is the value printed by the following C program?

#include<stdio.h>

int f(int *a, int n)
{
    if (n <= 0) return 0;
    else if (*a % 2 == 0) return *a+f(a+1, n-1);
    else return *a - f(a+1, n-1);
}

int main()
{
    int a[] = {12, 7, 13, 4, 11, 6};
    printf("%d", f(a, 6));
    return 0;
}

View worked solution

Answer: C

We can trace the recursive calls of the function f(a, n) starting from the base case where $n \le 0$ :

$f(a+6, 0) = 0$ (since $n \le 0$ )
$f(a+5, 1) = 6 + f(a+6, 0) = 6 + 0 = 6$ (since $6$ is even)
$f(a+4, 2) = 11 - f(a+5, 1) = 11 - 6 = 5$ (since $11$ is odd)
$f(a+3, 3) = 4 + f(a+4, 2) = 4 + 5 = 9$ (since $4$ is even)
$f(a+2, 4) = 13 - f(a+3, 3) = 13 - 9 = 4$ (since $13$ is odd)
$f(a+1, 5) = 7 - f(a+2, 4) = 7 - 4 = 3$ (since $7$ is odd)
$f(a, 6) = 12 + f(a+1, 5) = 12 + 3 = 15$ (since $12$ is even)

Therefore, the value printed by the program is 15.

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Published 10 Oct 2026

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