GATE | GATE-CS-2003 | Question 88

In the following C program fragment, j, k n and TwoLog_n are interger 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)⌉

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) {}

Answer: (B)

Explanation:

// Initialize all values as 0 
for (k = 3; k < = n; k++) 
    A[k] = 0; 
  
for (k = 2; k < = TwoLog_n; k++) 
    for (j = k + 1; j < = n; j++) 
        // If k divides j, then A[j] is  
        // set as 0, else non-zero 
        A[j] = A[j] || (j % k); 
  
// Print all numbers where A[j] is 0 
for (j = 3; j < = n; j++) 
    if (!A[j])  
        printf("%d", j); 

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