ISI2018-PCB-CS6

Question

The following function computes an array $SPF$, where, for any integer $1 < i < 1000$,  $SPF[i]$ is the smallest prime factor of $i$. For example, $SPF[6]$ is $2$, and $SPF[11]$ is $11$.

There are five missing parts in the following code, commented as $/* Blank */$. For each of them, copy the entire line with the comment and fill the blank appropriately in your answer sheet.

int SPF[1000];

void findSPF() {

    SPF[1] = 1;

    // Initializing SPF of every number to be itself

    for (int i = 2; i < 1000; i++) { 
        _____; /* Blank 1 */
    }

    // SPF of every even number is 2

    for (int i = 4; i < 1000; i += 2) {

        SPF[i] = _____; /* Blank 2 */ 
    }
    
    // For odd numbers, updating the SPFs of their multiples

    for (int i = _____; i * i < 1000; i++) {

    /* Blank 3 */

        if (SPF[i] == i) {

        // No smaller factor of i found yet

            for (int j = _____; j < 1000; j+= i) {

            /* Blank 4 */ 
                if (SPF[j] == j) {

                    SPF[j] = _____; /* Blank 5 */
                }
            }
        }
    }
}

 

Answer 1

1. int SPF[1000];
2.  
3. void findSPF() {
4.  
5. SPF[1] = 1;
6.  
7. // Initializing SPF of every number to be itself
8.  
9. for (int i = 2; i < 1000; i++) {
10. SPF[i]=i; /* Blank 1 */
11. }
12.  
13. // SPF of every even number is 2
14.  
15. for (int i = 4; i < 1000; i += 2) {
16.  
17. SPF[i] = 2; /* Blank 2 */
18. }
19.  
20. // For odd numbers, updating the SPFs of their multiples
21.  
22. for (int i = 3; i * i < 1000; i++) {
23.  
24. /* Blank 3 */
25.  
26. if (SPF[i] == i) {
27.  
28. // No smaller factor of i found yet
29.  
30. for (int j = i; j < 1000; j+= i) {
31.  
32. /* Blank 4 */
33. if (SPF[j] == j) {
34.  
35. SPF[j] = SPF[i]; /* Blank 5 */
36. }
37. }
38. }
39. }
40. }

Comments

Hi, can you explain what does last for loop do?

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For the last loop, it will update all the multiples of the smaller number i, to it's all the dividend j with the spf of i.

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check chatgpt...it has whole explanation