PAT Advanced 1096 Consecutive Factors (20分)

Posted 2021-03-13 littlepage

Among all the factors of a positive integer N, there may exist several consecutive numbers. For example, 630 can be factored as 3×5×6×7, where 5, 6, and 7 are the three consecutive numbers. Now given any positive N, you are supposed to find the maximum number of consecutive factors, and list the smallest sequence of the consecutive factors.

Input Specification:

Each input file contains one test case, which gives the integer N (1<N<).

Output Specification:

For each test case, print in the first line the maximum number of consecutive factors. Then in the second line, print the smallest sequence of the consecutive factors in the format factor[1]*factor[2]*...*factor[k], where the factors are listed in increasing order, and 1 is NOT included.

Sample Input:

630

 

Sample Output:

3
5*6*7

最大连乘因子，我们找的是最大连乘因子，所以，我们从2到sqrt(n)进行遍历，因为永远到不了sqrt(n)，

之后进行遍历计算。

#include <iostream>
#include <vector>
#include <cmath>
using namespace std;
int main(){
    long int N, sqrt_n;
    cin >> N;
    sqrt_n = sqrt(N);
    vector<int> m, tmp_v;
    for(int i = 2; i <= sqrt_n; i++){
        int cp_i = i, sum = i;
        while(N % sum == 0 && cp_i <= sqrt_n){
            tmp_v.push_back(cp_i);
            cp_i++;
            sum *= cp_i;
        }
        if(tmp_v.size() > m.size())
            m = tmp_v;
        tmp_v.clear();
    }
    if(m.size() == 0) cout << 1 << endl << N;
    else {
        cout << m.size() << endl;
        for(int i = 0; i < m.size(); i++)
            if(i != m.size() - 1) cout << m[i] << "*";
            else cout << m[i];
    }
    system("pause");
    return 0;
}