#include <iostream>
#include <cmath>
#include <array>
#include <vector>
#include <algorithm>

bool is_perfect(int num)
{
    int sum = 0;

    for (int i = 1; i < num; i++) // O(n)
    {
        // check if num is prime. prime numbers cannot be perfect.
        if (sum == 1 && i*i > num)
            return false;

        if (num % i == 0)
            sum += i;

        if (sum > num)
            return false;
    }

    return sum == num;
}

void test_case()
{
    std::array<int, 4> perfect_nums = {6, 28, 496, 8128};
    std::vector<int> fails;

    for (int i = 1; i <= 8128; i++)
    {
        bool perfect = (std::find(perfect_nums.cbegin(),perfect_nums.cend(), i) != perfect_nums.cend());

        bool result = is_perfect(i);

        if (result == perfect)
            std::cout << "OK for " << i << " is perfect == " << result << std::endl;
        else
        {
            std::cout << "FAIL for " << i << ". The result is " << result << " but should be " << perfect << std::endl;
            fails.push_back(i);
        }
    }

    if (fails.size())
    {
        std::cout << "\n\nTest failed for the number(s) ";
        for (int fail : fails)
            std::cout << fail << std::endl;
    }
    else
        std::cout << "\n\nThere are no failed tests!";
}

int main() {
    test_case();
    return 0;
}