GATE CS 2019 Q.62 (CS Q.52): Data Types, Operators and Control Flow

Consider the following C program:

#include <stdio.h>
int main() {
    float sum = 0.0, j = 1.0, i = 2.0;
    while (i/j > 0.0625) {
        j = j + j;
        sum = sum + i/j;
        printf("%f\n", sum);
    }
    return 0;
}

The number of times the variable sum will be printed, when the above program is executed, is ________.

Your answer

Official answer and solution

Official answer: 5
From: Official GATE 2019 answer key

Solution

Trace the values of variables $i$ and $j$ across iterations of the while loop to determine the exact number of iterations before termination.

We are given the code:

float sum = 0.0, j = 1.0, i = 2.0;
while (i/j > 0.0625) {
    j = j + j;
    sum = sum + i/j;
    printf("%f\n", sum);
}

Note that $0.0625 = \frac{1}{16} = 2^{-4}$ .

Let us trace each iteration of the loop:

Before loop: $i = 2.0, j = 1.0$ .
Iteration 1: Check $i/j = 2.0 / 1.0 = 2.0 > 0.0625$ (True). Inside loop: $j = 1.0 + 1.0 = 2.0$ ; $sum = 0.0 + 2.0/2.0 = 1.0$ . Print 1.
Iteration 2: Check $i/j = 2.0 / 2.0 = 1.0 > 0.0625$ (True). Inside loop: $j = 2.0 + 2.0 = 4.0$ ; $sum = 1.0 + 2.0/4.0 = 1.5$ . Print 2.
Iteration 3: Check $i/j = 2.0 / 4.0 = 0.5 > 0.0625$ (True). Inside loop: $j = 4.0 + 4.0 = 8.0$ ; $sum = 1.5 + 2.0/8.0 = 1.75$ . Print 3.
Iteration 4: Check $i/j = 2.0 / 8.0 = 0.25 > 0.0625$ (True). Inside loop: $j = 8.0 + 8.0 = 16.0$ ; $sum = 1.75 + 2.0/16.0 = 1.875$ . Print 4.
Iteration 5: Check $i/j = 2.0 / 16.0 = 0.125 > 0.0625$ (True). Inside loop: $j = 16.0 + 16.0 = 32.0$ ; $sum = 1.875 + 2.0/32.0 = 1.9375$ . Print 5.
Iteration 6: Check $i/j = 2.0 / 32.0 = 0.0625 > 0.0625$ (False, because the inequality is strict: $0.0625 > 0.0625$ is false). The loop terminates.

Therefore, the printf statement is executed and sum is printed exactly 5 times.

Final answer

Common trap

Treating the loop condition as $\ge 0.0625$ instead of strict inequality $>$ , which would allow a 6th iteration.

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

Source

Paper: GATE 2019 Computer Science and Information Technology (CS)
Question: 62 of 65, printed as CS Q.52
Section: Computer Science and Information Technology

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