Refactoring with Iterators: Prime Factors

Andrew Woodward recently posted a comparison of his test-driven Prime Factors solution to one written by Uncle Bob. In the comments, someone suggested that Andrew use an iterator instead so I thought I’d give it a try.

First, let’s repost the original code:

private const int SMALLEST_PRIME = 2;

public List<int> Generate(int i)
{
    List<int> primes = new List<int>();
    int divider = SMALLEST_PRIME;
    while (HasPrimes(i))
    {
        while (IsDivisable(i, divider))
        {
            i = AddPrimeToProductsAndReduce(i, primes, divider);
        }
        divider++;
    }
    return primes;
}

private bool IsDivisable(int i, int divider)
{
    return i%divider == 0;
}

private bool HasPrimes(int i)
{
    return i >= SMALLEST_PRIME;
}

private int AddPrimeToProductsAndReduce(int i, List<int> primes, int prime)
{
    primes.Add(prime);
    i /= prime;
    return i;
}

By switching our method to return IEnumerable<int>, we can replace the primes list with an iterator. We will also remove the AddPrimeToProducts functionality from that helper method since we don’t have the list any more:

public IEnumerable<int> Generate(int i)
{
    int divider = SMALLEST_PRIME;
    while (HasPrimes(i))
    {
        while (IsDivisable(i, divider))
        {
            yield return divider;
            i = Reduce(i, divider);
        }
        divider++;
    }
}

private int Reduce(int i, int prime)
{
    return i / prime;
}

I think this is a good change for three reasons:

  1. There’s nothing about the problem that requires a List<int> be returned, we just want a sequence of the factors.
  2. AddPrimeToProductsAndReduce suggested that it had a side effect, but exactly what wasn’t immediately obvious.
  3. It’s much easier to see what values are being included in the result.

That said, I think we can clean this up even more with a second iterator. Specifically, I think we should break out the logic for our candidate factors:

private IEnumerable<int> Divisors
{
    get
    {
        int x = SMALLEST_PRIME;
        while (true)
            yield return x++;
    }
}

Which allows us to separate the logic for generating a divider from the code that consumes it:

public IEnumerable<int> Generate(int toFactor)
{
    foreach (var divider in Divisors)
    {
        if (!HasPrimes(toFactor))
            break;

        while (IsDivisable(toFactor, divider))
        {
            yield return divider;
            toFactor = Reduce(toFactor, divider);
        }
    }
}

We should also eliminate the negation by flipping HasPrimes to become IsFactored:

public IEnumerable<int> Generate(int toFactor)
{
    foreach (var divider in Divisors)
    {
        if (IsFactored(toFactor))
            break;

        while (IsDivisable(toFactor, divider))
        {
            yield return divider;
            toFactor = Reduce(toFactor, divider);
        }
    }
}

private bool IsFactored(int i)
{
    return i <= 1;
}

This does introduce a (very) minor inefficiency in that the Divisors enumerator will MoveNext() one extra time before breaking out of the loop, which could be mitigated by checking IsFactored both before the foreach and after the while loop. Less readable, insignificantly more efficient…take your pick.

The other advantage to breaking out the logic to generate Divisors is that we can easily pick smarter candidates. One option is to skip even numbers greater than 2. An even better optimization takes advantage of the fact that all primes greater than 3 are of the form x±1 where x is a multiple of 6:

private IEnumerable<int> Divisors
{
    get
    {
        yield return 2;
        yield return 3;
        int i = 6;
        while (true)
        {
            yield return i - 1;
            yield return i + 1;
            i += 6;
        }
    }
}

Implementing this sort of logic in the original version would have been much more difficult, both in terms of correctness and readability.

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