GATE CS 2021 Set 1 Q.58 (CS Q.48): Data Types, Operators and Control Flow

Consider the following ANSI C function:

int SimpleFunction(int Y[], int n, int x)
{
    int total = Y[0], loopIndex;
    for (loopIndex = 1; loopIndex <= n - 1; loopIndex++)
        total = x * total + Y[loopIndex];
    return total;
}

Let $Z$ be an array of 10 elements with $Z[i]=1$ , for all $i$ such that $0 \le i \le 9$ . The value returned by SimpleFunction(Z, 10, 2) is __________

Your answer

Official answer and solution

Official answer: 1023
From: Official GATE 2021 answer key

Solution

Recognize the Horner's rule accumulator pattern and compute the resulting geometric series.

The function SimpleFunction(Y, n, x) initializes total = Y[0] and then iteratively updates:

\text{total} = x \cdot \text{total} + Y[i] \quad \text{for } i = 1, 2, \dots, n - 1

Expanding this recurrence yields Horner's rule representation for the polynomial:

\text{total} = Y[0] x^{n-1} + Y[1] x^{n-2} + \dots + Y[n-2] x + Y[n-1] = \sum_{i=0}^{n-1} Y[i] x^{n-1-i}

For the call SimpleFunction(Z, 10, 2), we have $n = 10$ , $x = 2$ , and $Z[i] = 1$ for all $0 \le i \le 9$ :

\text{total} = \sum_{i=0}^{9} 1 \cdot 2^{9-i} = \sum_{k=0}^{9} 2^k = 2^{10} - 1 = 1024 - 1 = 1023

Final answer

1023

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 (CS, Set-1)
Question: 58 of 65, printed as CS Q.48
Section: Computer Science and Information Technology

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