UniquePrimeFactorization

#include <cmath>
#include <iostream>

using namespace std;

unsigned prime_factors(unsigned max, unsigned** factors)
{
    if (max < 2) {
        return -1;
    }

    // find all prime factors

    bool* is_composite = new bool[max + 1] { false };
    double sup = sqrt(max) + 1;

    for (size_t i = 3; i <= sup; i += 2) {
        if (!is_composite[i]) {
            for (size_t j = 3; i * j <= max; j += 2) {
                is_composite[i * j] = true;
            }
        }
    }

    // calculate the number of prime factors

    unsigned count = 1;

    for (size_t i = 3; i <= max; i += 2) {
        count += !is_composite[i];
    }

    // allocate space and fill in the prime factors

    if (factors != nullptr) {
        *factors = new unsigned[count];

        unsigned index = 0;
        (*factors)[index++] = 2;

        for (size_t i = 3; i <= max; i += 2) {
            if (!is_composite[i]) {
                (*factors)[index++] = i;
            }
        }
    }

    delete[] is_composite;
    return count;
}

int main(int argc, char const* argv[])
{
    unsigned* factors = nullptr;
    unsigned factors_cnt = prime_factors(100, &factors);

    unsigned N;
    cin >> N;

    unsigned exponents[100] = { 0 };

    for (size_t i = 0; i < factors_cnt; i++) {
        while (N % factors[i] == 0) {
            exponents[i]++;
            N /= factors[i];
        }
    }

    for (size_t i = 0; i < factors_cnt; i++) {
        cout << factors[i] << "\t" << exponents[i] << endl;
    }
    cout << N << endl;

    if (factors != nullptr) {
        delete[] factors;
    }

    return 0;
}