GATE CS 2021 Set 2 Q.33 (CS Q.23): Functions, Recursion, Scope and Storage Classes

Consider the following ANSI C function:

int SomeFunction(int x, int y)
{
    if ((x == 1) || (y == 1)) return 1;
    if (x == y) return x;
    if (x > y) return SomeFunction(x - y, y);
    if (y > x) return SomeFunction(x, y - x);
}

The value returned by SomeFunction(15, 255) is ______.

Your answer

Official answer and solution

Official answer: 15
From: Official GATE 2021 answer key

Solution

Recognize the recursive function as Euclid's subtraction-based algorithm for finding the greatest common divisor (GCD).

Analyzing SomeFunction(x, y):

If $x=1$ or $y=1$ , it returns 1 (coprime).
If $x=y$ , it returns $x$ .
If $x > y$ , it recurses on $(x - y, y)$ .
If $y > x$ , it recurses on $(x, y - x)$ .

This is the classic Euclidean algorithm by repeated subtraction, which computes $\gcd(x, y)$ .

For inputs $x = 15$ and $y = 255$ :
Since $255 = 15 \times 17$ , $y$ is an exact multiple of $x$ . Repeatedly subtracting 15 from $y$ reduces $y$ by 15 in each step: $255 \to 240 \to 225 \dots \to 15$ .

When $y$ reaches 15, the condition x == y evaluates to true ( $15 == 15$ ) and returns $15$ .

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2021 Computer Science and Information Technology - Session 2 (CS2)
Question: 33 of 65, printed as CS Q.23
Section: Computer Science and Information Technology

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