1059.Prime Factors

题目描述

Given any positive integer N, you are supposed to find all of its prime factors, and write them in the format N = p​1​​ ^ k​1​​ ​​ ×p​2​​ ^ ​k​2​​ ​​ ×⋯×p​m​​ ^ ​k​m​​ ​​ .

Input Specification:

Each input file contains one test case which gives a positive integer N in the range of long int.

Output Specification:

Factor N in the format N = p​1​​ ^k​1​​ *p​2​​ ^k2​​ *…*p​m​​ ^k​m​​ , where p​i​​ 's are prime factors of N in increasing order, and the exponent k​i​​ is the number of p​i​​ -- hence when there is only one p​i​​ , k​i​​ is 1 and must NOT be printed out.

Sample Input :

97532468

Sample Output:

97532468=2^211171011291

考点

素数表建立

思路

1.建立素数表
2.从2开始判断该数是否为素数且是否能被p整除

代码

#include 
#include 
using namespace std;
vector prime(500000, 1);
int main() {
    for (int i = 2; i*i <= 500000; i++)
        for (int j = 2; j*j <= 500000; j++)
            prime[i*j] = 0;
    long int p;
    scanf("%ld", &p);
    printf("%ld=", p);
    if (p == 1) cout << "1";
    bool state = false;
    for (int i = 2; p >= 2; i++) {
        int cnt = 0, flag = 0;
        while (prime[i] == 1 && p%i == 0) {
            cnt++;
            p = p / i;
            flag = 1;
        }
        if (flag) {
            if (state) cout << "*";
            cout << i;
            state = true;
        }
        if (cnt >= 2)
            printf("^%d", cnt);
    }
    return 0;
}