Sieve of Eratosthenes algorithm

Question

I am currently reading \"Programming: Principles and Practice Using C++\", in Chapter 4 there is an exercise in which:

I need to mak

Answer 1

Think of the sieve as a set.
Go through the set in order. For each value in thesive remove all numbers that are divisable by it.

#include 
#include 
#include 
#include 


typedef std::set   Sieve;

int main()
{
    static int const max = 100;

    Sieve   sieve;

    for(int loop=2;loop < max;++loop)
    {
        sieve.insert(loop);
    }


    // A set is ordered.
    // So going from beginning to end will give all the values in order.
    for(Sieve::iterator loop = sieve.begin();loop != sieve.end();++loop)
    {
        // prime is the next item in the set
        // It has not been deleted so it must be prime.
        int             prime   = *loop;

        // deleter will iterate over all the items from
        // here to the end of the sieve and remove any
        // that are divisable be this prime.
        Sieve::iterator deleter = loop;
        ++deleter;

        while(deleter != sieve.end())
        {
            if (((*deleter) % prime) == 0)
            {
                // If it is exactly divasable then it is not a prime
                // So delete it from the sieve. Note the use of post
                // increment here. This increments deleter but returns
                // the old value to be used in the erase method.
                sieve.erase(deleter++);
            }
            else
            {
                // Otherwise just increment the deleter.
                ++deleter;
            }
        }
    }

    // This copies all the values left in the sieve to the output.
    // i.e. It prints all the primes.
    std::copy(sieve.begin(),sieve.end(),std::ostream_iterator(std::cout,"\n"));

}