CSCI 340 assign 3

//terina burr
//section one
//assignment three
//due 9/21/15

#include <iostream>
#include <set>
#include <cstdlib>
#include <iomanip>

using namespace std;

int ITEM_W = 5;
int NO_ITEMS =10;

void sieve( set<int>& s, int n) ;

void print_primes( const set<int>& s) ;

int main() {
    set<int> s;
    sieve(s, 1000);
    print_primes(s);
    return 0;
}

/***************************************************************
Function: sieve

Use:      it applies the sieve of eratosthesis algorithm to take out all the numbers that are not prime

Arguments:  1. s: the set that you are going to go through
        2. n:  the last number in the set

Returns:   nothing
***************************************************************/


void sieve(set <int> &s, int n)
{
    int m, i;
    s.erase(s.begin(), s.end());
//erases everything that is in the set
    for(m =2; m<n; m++)
        s.insert(m);
//inserts m if it is less than  the limit
    for(m=2; m*m<=n; m++)
//finds all number using the sieve of erat
//it looks at the numbers from 2 to m*m<=2
        if(s.find(m) !=s.end())
        {
//checks to see if m is in the set
            i=2*m;
//if not then it removes multiples of m starting with 2*m
            while (i<=n)
            {
                s.erase(i);
                i+=m;
//i is multiples of m
            }
        }
}

/***************************************************************
Function: print_primes

Use:      prints all items in the set with NO_ITEMS per line and ITEM_W on how far apart they are

Arguments:  1. s: the set that you are going to go through
Returns:   nothing
***************************************************************/


void print_primes(const set<int> &s)
{
    set<int>::iterator iter;
    int count =0;
    iter = s.begin();
    cout << "There are " << s.size() << " prime numbers: " <<endl;
    while(iter !=s.end())
    {
        count++;
        cout << setw(ITEM_W) << *iter;
//prints the numbers at a width that is four spaces apart
            if(count % NO_ITEMS == 0)
            {
                cout <<endl;
            }
//if there is more than 16 numbers on a line then they start a new line
        iter++;
    }
cout<<endl;




}