判断一个数是否为素数

#include<iostream>
#include<vector>
#include<math.h>
#include<algorithm>/*判断是否为素数*/
bool isprime(int n)
{bool result;int k = (int)sqrt((double)n); // 只需要循环到 √n 即可int i = 0;for (i = 2; i <= k; i++){if (n%i == 0)break;}result = (i > k);return result;
}void test_isprime()
{std::cout << " isprime(2) = " << isprime(2) << '\n';std::cout << " isprime(10) = " << isprime(10) << '\n';std::cout << " isprime(17) = " << isprime(17) << '\n';
}

求一个数的因数

/* 寻找所有因数 包括1和其本身*/
std::vector<int> factorize(int n)
{std::vector<int> answer;int k = (int)sqrt((double)n);int i = 0;for (i = 1; i <= k; i++){if (!(n%i)){answer.push_back(i);answer.push_back(n / i);}}sort(answer.begin(), answer.end()); // 利用sort函数进行排序，再输出，这一步若不是必须可省略std::cout << " The factors of " << n << " are";return answer;
}/* 打印vector */
void print_vector(std::vector<int>& vec)
{for (auto it = vec.cbegin(); it != vec.cend(); ++it)std::cout << ' ' << *it;std::cout << '\n';
}void test_factorize()
{std::vector<int> vf;vf = factorize(2);print_vector(vf);vf = factorize(72);print_vector(vf);vf = factorize(196);print_vector(vf);
}

质因数分解

/* 质因数分解 */
std::vector<int> prime_factorize(int n)
{std::vector<int> answer;if (n != 2){int k = (int)sqrt((double)n); // 只需要循环到 √n 即可int i = 0, m = n;for (i = 2; i <= k; i++){while (m%i == 0){m = m / i;answer.push_back(i);}if (m == n)answer.push_back(n);}}elseanswer.push_back(n);std::cout << " The prime factorization of " << n << " are";return answer;
}void test_prime_factorize()
{std::vector<int> vf;vf = prime_factorize(2);print_vector(vf);vf = prime_factorize(72);print_vector(vf);vf = prime_factorize(196);print_vector(vf);
}int main()
{test_isprime();test_factorize();test_prime_factorize();return 0;
}

结果