PAT Advanced 1059 Prime Factors (25分)

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

这道题我们用素数表存储500000个素数，进行筛选。

之后我们进行计数即可。

我们要注意的是格式化，以及1这个情况，否则会打印1=，实际上应该1=1

#include <iostream>
#include <vector>
#include <map>
#define M 500000
using namespace std;
vector<bool> v(M, 1); // prime table
map<int, int> m;
int main() {
    int N;
    scanf("%d", &N);
    printf("%d=", N);
    if(N == 1) printf("1");
    for(int i = 2; i * i < M; i++)
        for(int j = 2; j * i < M; j++)
            v[i * j] = 0;
    for(int i = 2; i < M && N != 1; i++) {
        while(v[i] && N % i == 0 && N != 1) {
            m[i]++;
            N /= i;
        }
    }
    bool start = true;
    for(auto it = m.begin(); it != m.end(); it++) {
        if(it->second >= 1) {
            if(!start) printf("*");
            if(it->second == 1) printf("%d", it->first);
            if(it->second > 1) printf("%d^%d", it->first, it->second);
            start = false;
        }
    }return 0;
}