#include <iostream>
#include <string>
#include <vector>
#include <cmath>

// use generics for a reusable method
template <typename number>
std::string create_overflow() {
    number next = 2;
    number valid = 0;
    number iter = 0;

    while(true) {
        next = next * 2;
        if(valid > next) {
            std::string message = typeid(number).name();
            message += " overflow occurred: 2**" + std::to_string(iter) + " = " + std::to_string(next);
            message += " should be bigger as 2**" + std::to_string(iter - 1) + " != " + std::to_string(valid);
            return message;
        }
        iter++; valid = next;
    }
}

std::vector<bool> sieve_of_eratosthenes(int limit) {
    // avoid edge cases limit=0 or limit=1
    int length = limit + 2;

    // preparation of a bool vector
    std::vector<bool> primes(length, true);
    primes[0] = false;
    primes[1] = false;

    // calculate sieve
    for(int i = 2; i <= std::sqrt(limit); i++) {
        if(primes[i]) {
            for(int p = i * i; p <= limit; p += i) {
                primes[p] = false;
            }
        }
    }
    return primes;
}

/*
 * Anmerkung:
 * Ich mag es nicht wirklich Pointer in C++ zu benutzen. Deshalb verwende ich die Klassen std::string und std::vector
 * um zu verhindern, dass die Funktionen bool* bzw. char* pointer ausgeben müssen.
 */
int main() {
    std::cout << create_overflow<short>() << std::endl;
    std::cout << create_overflow<int>() << std::endl;
    std::cout << create_overflow<long>() << std::endl;

    int limit = 100;
    std::vector<bool> primes = sieve_of_eratosthenes(limit);
    std::cout << "Prime numbers up to " << limit << " are: ";
    for (int i = 0; i < limit; ++i) {
        if (primes[i]) {
            std::cout << i << " ";
        }
    }
    std::cout << std::endl;

    return 0;
}