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GATE 2021 CS – Question 58

Programming and Data Structures · Programming in C · 2 marks · Numerical answer

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 ______.

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Correct answer: 1023

Explanation

This is Horner's rule for the polynomial with all coefficients 1 evaluated at x=2: $2^9+2^8+\dots+1 = 2^{10}-1 = 1023$.