Analysis of the real questions of the CSP-J preliminary competition over the years | 2022 CSP-J preliminary competition perfect procedure (35-39)

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Print all positive factors of positive integer n from small to large.

Try to complete the enumeration procedure.

#include <bits/stdc++.h>
using namespace std;

int main() {
    int n;
    cin >> n;

    vector<int>fac;
    fac.reserve((int)ceil(sqrt(n)));  //为fac申请一片内存空间，对程序理解无影响
    
    int i;
    for (i=1; i*i<n; ++i) {  //此循环是将小于√n的所有因数放入到fac中
        if (①) {
            fac.push_back(i);  
        }
    }

    for (int k=0; k<fac.size(); ++k) {  //将fac中已经存放的数据打印出来
        cout << ② << "";
    }
    if (③) {  //如果不能理解可以先跳过3、4直接看第5个空。这里用来处理i*i=n的数
        cout << ④ << "";
    }
    for (int k=fac.size()-1; k>=0; --k) {  //逆序枚举fac
        cout << ⑤ << "";
    }
}

35. Place ① should be filled in ( )

A.n % i == 0

B.n % i == 1

C.n % (i-1) == 0

D.n % (i-1) == 1

[Answer]: A

【Analysis】

The topic is to find the factor of n, so when it is a factor of n here, put it in fac. So choose A

36. Place ② should be filled in ( )

Year / year[k]

B.fac[k]

C.fac[k]-1

Dn / (fac[k]-1)

[Answer]: B

【Analysis】

Print out the factor of the small fish √n that has been put into fac

37. Place ③ should be filled in ( )

A.(i-1) * (i-1) == n

B.(i-1) * i == n

C.i * i == n

D.i * (i-1) == n

[Answer]: C

【Analysis】

If n=9, the output before line 16 is 1, and the output from line 24 to 26 is 9, and there is still a 3 missing, so the combination of 3 and 4 should be able to output 3. Because 3*3=9, so roll it backwards and choose C

38. Place ④ should be filled in ( )

A.n-i

B.n-i+1

C.i-1

D.i

[Answer]: D

【Analysis】

Same as question 37, output this i, that is, √n

39, ⑤ should be filled in ( )

Year / year[k]

B.fac[k]

C.fac[k]-1

Dn / (fac[k]-1)

[Answer]: A

【Analysis】

If n=6, its positive factors are 1, 2, 3, 6, 1 and 2 are stored in fac before line 16, and 3 and 6 can be obtained by n/fac[k], so choose A