在C＃中将共享相同父项和子项的项目分组

Question

I wish to find an efficient way to group the items in a tree graph which has the following characteristics:

About the tree graph, it has multiple layers like this, if drawn horizontally:

(0,0)--(1,0)--(2,0)
   \ \-(1,1)--(2,1)
    \--(1,2)--/

1. For a node (x,y) modeled by a class Node, x is its "level" while y is its "index". For any edge we only allow sequential indexes for the two nodes of this edge, so (1,2)-(3,2) is forbidden.
2. Allow multiple roots: (0,0) (0,1) ...etc.

About "group the items": Because in the data source of the tree there are nodes like:

(3,5)--(4,10)--(5,5)
  \  \-(4,11)-/  /
   \    ....    /
    \--(4,80)--/

I wish to group the nodes like those (4,10~80) above into one node, which these nodes share the same characteristics

1. has only 1 parent node which they share
2. has only 1 child node which they share
3. Also need to tackle the case which they only have a common parent (or a common child) but have no children (or parents) at all.

using a special class CompoundNode, a subclass of Node.

Here is a skeleton class for Node:

public class Node
{
    public Node(string id)
    {
        Id = id;
    }

    public string Id { get; set; }

    private readonly List<Node> children = new List<Node>();
    public List<Node> Children { get { return children; } }
    private readonly List<Node> parents = new List<Node>();
    public List<Node> Parents { get { return parents; } }

    protected bool Equals(Node other)
    {
        ....
    }

    public override bool Equals(object obj)
    {
        ....
    }

    public override int GetHashCode()
    {
        return (Id != null ? Id.GetHashCode() : 0);
    }

    public override string ToString()
    {
        ....
    }
}

Thanks!

EDIT:

Here is the solution i did (extracts the relationship without modifying the tree), without tackling the situation of zero parent or zero child:

        var relationships = new List<Tuple<string, string, string>>();

        foreach (var middle in nodes)
        {
            if (middle.Children.Count == 1 && middle.Parents.Count == 1)
            {
                var child = middle.Children[0];
                var parent = middle.Parents[0];
                relationships.Add(new Tuple<string, string, string>(parent.Id, middle.Id, child.Id));
            }
        }
        var groups = relationships.GroupBy(t => new { t.Item1, t.Item3 }).Where(a => a.Count() > 1);

        var toGroupedRelations = groups.Cast<IEnumerable<Tuple<string, string, string>>>().ToList();

Answer 1

Ok - here's a first attempt. Should give you some good pointers anyway:

var nodes = new List<Node>();

// !! populate your nodes list with all your real nodes first!

// filter to nodes with at most 1 parent and 1 child
// group by a tuple containing the parent (if it exists) and the child (if it exists)
var grouped = nodes.Where(i => i.Children.Count <= 1 && i.Parents.Count <= 1)
    .GroupBy(i => 
        new Tuple<Node, Node>(i.Parents.Count == 0 ? null : i.Parents[0], 
                                i.Children.Count == 0 ? null : i.Children[0]));

// go through your groups - each one should be a cluster of nodes to be merged
foreach (var group in grouped)
{
    // get the first node in the group (which one is arbitrary if we're merging anyway)
    var node = group.First();

    // if this group has a parent
    if (node.Parents.Count == 1)
    {
        // change the parent to only have one child - this one!
        node.Parents[0].Children.Clear();
        node.Parents[0].Children.Add(node);
    }

    // if this group has a child
    if (node.Children.Count == 1)
    {
        // change the child to only have one parent - this one!
        node.Children[0].Parents.Clear();
        node.Children[0].Parents.Add(node);
    }
}