Analysis of past CSP-J preliminary competition questions | 2020 CSP-J preliminary competition improvement procedures (34-38)

Learn C++ from a young age! Record the questions in the CSP-J exam preparation study process and record every moment.

Attached is a summary post: Analysis of past CSP-J preliminary test questions | Summary_csp past past questions_Blog of a communicator who loves programming-CSDN blog

---

(Prime factorization) Given a positive integer n, please output the result of decomposing n into prime factors. The results are output from small to large.

For example: input n=120, the program should output 2 2 2 3 5, which means 120=2×2×2×3×5. The input guarantee is 2≤n≤10^9. Tip: First enumerate the variable i from small to large, and then use i to divide n continuously to find all prime factors.

Try the completion program.

#include <cstdio>
using namespace std;

int n, i;

int main() {
    scanf("%d", &n);
    for (i = ①; ② < = n; i ++) {
        ③ {
            printf("%d ", i);
            n = n / i;
        }
    }
    if(④)
        printf("%d ", ⑤);
    return 0;
}

34. ① should be filled in ( )

A.1

B.n-1

C.2

D.0

[Answer]: C

【Analysis】

For each factor starting from 2, use it to divide n, choose C

35. ② should be filled in ( )

A.n / i

B.n / (i * i)

C.i * i

D.i * i * i

[Answer]: B

【Analysis】

Prime factorization only tries to divide those prime factors less than or equal to √n, choose B

36. ③ should be filled in ( )

A.if (n % i == 0)

B.if (i * i <= n)

C.while (n % i == 0)

D.while (i * i <= n)

【Answer】:

【Analysis】

If n%i==0, divide repeatedly to obtain multiple prime factors, choose C

37. ④ should be filled in ( )

A.n > 1

B.n <= 1

C.i < n / i

D.i + i <= n

【Answer】:A

【Analysis】

After trying to divide all factors less than or equal to √n, n is still left (it has not been divided into 1), which means that the value of n at this time is the only prime factor greater than √n.

38. ⑤ should be filled in ( )

A.2

B.n / i

C.n

D.i

[Answer]: C

【Analysis】

Refer to question 4, n should be output at this time. For example, when n=5, output 5