PAT_甲级_1059

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1059 Prime Factors

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​​ ​km​​ ​​ .

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​​ ^k1​​ *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=2^211171011291

注意特例7 = 7， 1 = 1。

#include<iostream>
#include<stdio.h>
#include<math.h>
#include<vector>
#include<map>
using namespace std;
vector<long long int> arr_prime;
map<long long, int> info;
long long Is_prime(long long a)
{
    if (a <= 1) return 0;
    for (long long i = 2; i <= int(sqrt(a)); i++) {
        if (a % i == 0) {
            return 0;
        }
    }
    return 1;
}
int main()
{
    long long num;
    cin >> num;
    if (num == 1) {
        cout << "1=1" << endl;
        return 0;
    }
    for (long long i = 2; i <= int(sqrt(num)); i++) {
        if (Is_prime(i)) {
            arr_prime.push_back(i);
            info[i] = 0;        }
    }
    arr_prime.push_back(num);
    info[num] = 0;
    long long num_2 = num;
    for (long long i = 0; i <= arr_prime.size(); i++) {
        while (1) {
            if (num_2 % arr_prime[i] == 0) {
                num_2 = num_2 / arr_prime[i];
                info[arr_prime[i]]++;
            } else {
                break;
            }
        }
        if (num_2 == 1) {
            break;
        }
    }
    cout << num << '=';
    int flag_1 = 0;
    if (info[arr_prime[0]] == 1) {
        cout << arr_prime[0];
        flag_1 = 1;
    } else if (info[arr_prime[0]] > 1) {
        flag_1 = 1;
        cout << arr_prime[0] << '^' << info[arr_prime[0]];
    }
    for (long long i = 1; i <= arr_prime.size(); i++) {
        if (flag_1 == 0) {
            if (info[arr_prime[i]] == 1) {
                cout << arr_prime[i];
                flag_1 = 1;
            } else if (info[arr_prime[i]] > 1) {
                flag_1 = 1;
                cout << arr_prime[i] << '^' << info[arr_prime[i]];
            }
            continue;
        }
        if (info[arr_prime[i]] == 1) {
            cout << '*' << arr_prime[i];
        } else if (info[arr_prime[i]] > 1) {
            cout << '*' << arr_prime[i] << '^' << info[arr_prime[i]];
        } else {
            continue;
        }
    }
    cout << endl;
    return 0;
}