writing a custom comparer for linq groupby

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The grouping algorithm (and I think all LINQ methods) using an equality comparer always first compares hash codes and only executes Equals if two hash codes are equal. You can see that if you add tracing statements in the equality comparer:

class PointComparer : IEqualityComparer<Point>
{
    public bool Equals(Point a, Point b)
    {
        Console.WriteLine("Equals: point {0} - point {1}", a, b);
        return Math.Abs(a.X - b.X) < 1.0;
    }

    public int GetHashCode(Point point)
    {
        Console.WriteLine("HashCode: {0}", point);
        return point.X.GetHashCode()
            ^ point.Y.GetHashCode();
    }
}

Which results in:

HashCode: (1.1, 0)
HashCode: (4.1, 0)
HashCode: (1.2, 0)
HashCode: (4.1, 0)
Equals: point (4.1, 0) - point (4.1, 0)
(1.1, 0), 
(4.1, 0), (4.1, 0), 
(1.2, 0),

Only for the two points with equal hash codes Equals was executed.

Now you could trick the comparison by always returning 0 as hash code. If you do that, the output will be:

HashCode: (1.1, 0)
HashCode: (4.1, 0)
Equals: point (1.1, 0) - point (4.1, 0)
HashCode: (1.2, 0)
Equals: point (4.1, 0) - point (1.2, 0)
Equals: point (1.1, 0) - point (1.2, 0)
HashCode: (4.1, 0)
Equals: point (4.1, 0) - point (4.1, 0)
(1.1, 0), (1.2, 0), 
(4.1, 0), (4.1, 0),

Now for each pair Equals was executed, and you’ve got your grouping.

But…

What is “equal”? If you add another point (2.1, 0.0), which points do you want in one group? Using the symbol ≈ for the fuzzy equality, we have –

1.1 ≈ 1.2
1.2 ≈ 2.1

but

1.1 !≈ 2.1

This means that 1.1 and 2.1 will never be in one group (their Equals never passes) and that it depends on the order of the points whether 1.1 or 2.1 are grouped with 1.2.

So you’re on a slippery slope here. Clustering points by proximity is far from trivial. You’re entering the realm of cluster analysis.

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