GATE | GATE-CS-2003 | Question 88

In the following C program fragment, j, k n and TwoLog_n are integer variables, and A is an array of integers. The variable n is initialized to an integer ≥ 3, and TwoLog_n is initialized to the value of 2*⌈log2(n)⌉ 

C

for (k = 3; k < = n; k++)
    A[k] = 0;
for (k = 2; k < = TwoLog_n; k++)
    for (j = k + 1; j < = n; j++)
        A[j] = A[j] || (j % k);
for (j = 3; j < = n; j++)
    if (!A[j]) printf(\"%d\", j);

The set of numbers printed by this program fragment is

(A)

{m | m ≤ n, (∃ i) [m = i!]} Here i! mean factorial of i

(B)

{m | m ≤ n, (∃ i) [m = i²]}

(C)

{m | m ≤ n, m is prime}

(D)

Last print never executes

Answer: (D)

Explanation:

Option (D) is correct because if take n=4 then TwoLog_n value 4. first loop initially A[3]=A[4]=0; then two loop k = 2 to 4 and j = 3 to 4

if k=2 
         j=3  A[3] = A[3] || (3%2) 
                          = 0 || 1
                  A[3] = 1 
       j=4  A[4] = A[4] || (4%2)
                         = 0 || 0
                A[4] = 0
K=3
         j=4  A[4] = A[4] || (4%3)

                        = 0 || 1
               A[4] = 1
K=4
     J=5 condition false means terminate
 A[3] = A[4] = 1

Means last print loop never execute.

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