Com S 229 Spring 2007 Dr. Markus Lumpe
1
Problem Set 3: Classes, Constructors, and Destructors
Problem 1
Sieve of Eratosthenes:
We start with the integer number 2, which is the first prime. To obtain the rest of
the primes, we continue by filtering the multiples of 2 from the rest of the
integers. This leaves a list beginning with 3, which is the next prime. Now we
filter the multiples of 3 from the rest of that list. This leaves a list beginning with
5, which is the next prime, and so on.
In other words, we construct the primes by a sieving process, described as
follows: To sieve the integer numbers from 2 to N, build a list of prime filters,
whose first element is a filter for the integer 2 and the rest of which is obtained
by filtering all multiples of 2 out of the rest to N and generating a new prime
filter for each new prime number found:
Implement a C++ console application that defines a prime filter as outlined above. In
order to implement the application define the following two classes:
class Filter
{
private:
Sieve& fSieve;
int fPrime;
Filter* fNext;
static int fNumberOfFilters;
public:
Filter( Sieve& aSieve, int aPrime );
~Filter();
void check( int aNumber );
int getNumber();
static int getNumberOfPrimes();
};
