1059 Prime Factors (25)（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

素数的应用，用的是厄拉多塞素数筛选法，效率比较高。可见 https://blog.csdn.net/qq_34649947/article/details/79649247

#include <bits/stdc++.h>
using namespace std;
const int maxn = 100000 + 10;
int is_prime[maxn + 10];
int pNum = 0;
vector<int> prime;
void get_prime() {
    for (int i = 2; i <= maxn; i++) {
        is_prime[i] = 1;
    }
    for (int i = 2; i*i <= maxn; i++) {
        if (is_prime[i]) {
            for (int j = i*i; j <= maxn; j += i) {
                is_prime[j] = 0;
            }
        }
    }
    for (int i = 2; i <= maxn; i++) {
    	if (is_prime[i]) {
    		pNum++;//在最大范围内所有的质数的数量
    		prime.push_back(i);//存储所有的质因子
    	}
    }
}
//题目要求有底数和指数，所有用一个结构体来存
struct factor {
	int x;//质因子
	int cnt;//个数
}fac[100];
int n;
int main() {
	get_prime();
	int n, num = 0;//num为不同质因子的个数
	cin >> n;
	if (n == 1) cout << "1=1" << endl;
	else {
		cout << n << "=";
		int sqr = (int)(sqrt(1.0*n));
		//枚举
		for (int i = 0; i < pNum && prime[i] <= sqr; i++) {
			if (n % prime[i] == 0) {
				fac[num].x = prime[i];
				fac[num].cnt = 0;
				while (n % prime[i] == 0) {
					fac[num].cnt++;
					n /= prime[i];
				}
				num++;
			}
			if (n == 1) break;//退出循环
		}
		//注意点，最后一个样例
		if (n != 1) {//如果无法被根号n以内的质因子除尽,那就是质因子本身;
			fac[num].x = n;
			fac[num].cnt = 1;//
			num++;
		}
		for (int i = 0; i < num; i++) {
			if (i > 0) cout << "*";
			cout << fac[i].x;
			if (fac[i].cnt > 1) {
				cout << "^" << fac[i].cnt;
			}
		}
	}
	return 0;

}

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1059 Prime Factors (25)（25 分)

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