【笨方法学PAT】1059 Prime Factors （25 分）

一、题目

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​​^k​2​​*…*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=2^2*11*17*101*1291

二、题目大意

因式分解。

三、考点

素数表

四、注意

1、使用笨方法建立素数表，严重超时，记住这个建立素数表的方法；

2、参考：https://www.liuchuo.net/archives/2289。

五、代码

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