Algorithm to select groups of similar items in 2d array

Posted by mafutrct on Stack Overflow See other posts from Stack Overflow or by mafutrct
Published on 2010-05-07T12:07:10Z Indexed on 2010/05/07 12:28 UTC
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There is a 2d array of items (in my case they are called Intersections).

A certain item is given as a start. The task is to find all items directly or indirectly connected to this item that satisfy a certain function.

So the basic algorithm is like this:

Add the start to the result list. Repeat until no modification: Add each item in the array that satisfies the function and touches any item in the result list to the result list.

My current implementation looks like this:

private IList<Intersection> SelectGroup (
    Intersection start,
    Func<Intersection, Intersection, bool> select)
{
    List<Intersection> result = new List<Intersection> ();

    Queue<Intersection> source = new Queue<Intersection> ();
    source.Enqueue (start);

    while (source.Any ()) {
        var s = source.Dequeue ();
        result.Add (s);

        foreach (var neighbour in Neighbours (s)) {
            if (select (start, neighbour)
                && !result.Contains (neighbour)
                && !source.Contains (neighbour)) {
                source.Enqueue (neighbour);
            }
        }
    }

    Debug.Assert (result.Distinct ().Count () == result.Count ());
    Debug.Assert (result.All (x => select (x, result.First ())));

    return result;
}

private List<Intersection> Neighbours (IIntersection intersection)
{
    int x = intersection.X;
    int y = intersection.Y;

    List<Intersection> list = new List<Intersection> ();

    if (x > 1) {
        list.Add (GetIntersection (x - 1, y));
    }
    if (y > 1) {
        list.Add (GetIntersection (x, y - 1));
    }
    if (x < Size) {
        list.Add (GetIntersection (x + 1, y));
    }
    if (y < Size) {
        list.Add (GetIntersection (x, y + 1));
    }

    return list;
}

(The select function takes a start item and returns true iff the second item satisfies.)

This does its job and turned out to be reasonable fast for the usual array sizes (about 20*20). However, I'm interested in further improvements. Any ideas?

Example (X satisfies in relation to other Xs, . does never satisfy):

....
XX..
.XX.
X...

In this case, there are 2 groups: a central group of 4 items and a group of a single item in the lower left. Selecting the group (for instance by starting item [2, 2]) returns the former, while the latter can be selected using the starting item and sole return value [0, 3].

Example 2:

.A..
..BB
A.AA

This time there are 4 groups. The 3 A groups are not connected, so they are returned as separate groups. The bigger A and B groups are connected, but A does not related to B so they are returned as separate groups.

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