/**
* @file
* @brief C++ Program to calculate number of divisors
*
* This algorithm use the prime factorization approach.
* Any number can be written in multiplication of its prime factors.
*
Let N = P1^E1 * P2^E2 ... Pk^Ek
*
Therefore. number-of-divisors(N) = (E1+1) * (E2+1) ... (Ek+1).
*
Where P1, P2 ... Pk are prime factors and E1, E2 ... Ek are exponents
respectively.
*
* Example:-
*
N = 36
*
36 = (3^2 * 2^2)
*
number_of_positive_divisors(36) = (2+1) * (2+1) = 9.
*
list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
*
* Similarly if N is -36 at that time number of positive divisors remain same.
*
* Example:-
*
N = -36
*
-36 = -1 * (3^2 * 2^2)
*
number_of_positive_divisors(-36) = (2+1) * (2+1) = 9.
*
list of positive divisors of -36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
*
**/
#include
#include
/**
* Algorithm
*/
int number_of_positive_divisors(int n) {
std::vector prime_exponent_count;
for (int i = 2; i * i <= n; i++) {
int prime_count = 0;
while (n % i == 0) {
prime_count += 1;
n /= i;
}
if (prime_count != 0) {
prime_exponent_count.push_back(prime_count);
}
}
if (n > 1) {
prime_exponent_count.push_back(1);
}
int divisors_count = 1;
for (int i = 0; i < prime_exponent_count.size(); i++) {
divisors_count = divisors_count * (prime_exponent_count[i] + 1);
}
return divisors_count;
}
/**
* Main function
*/
int main() {
int n;
std::cin >> n;
if (n < 0) {
n = -n;
}
if (n == 0) {
std::cout << "All non-zero numbers are divisors of 0 !" << std::endl;
} else {
std::cout << "Number of positive divisors is : ";
std::cout << number_of_positive_divisors(n) << std::endl;
}
}