diff --git a/math/number_of_positive_divisors.cpp b/math/number_of_positive_divisors.cpp new file mode 100644 index 000000000..48ab63c36 --- /dev/null +++ b/math/number_of_positive_divisors.cpp @@ -0,0 +1,66 @@ +/// C++ Program to calculate number of divisors. + +#include +#include + +/** + * 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. + * +**/ + +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; +} + +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; + } +}