Tree.java

class Item {
	public int Id;
	public ArrayList<int> TransactionIds;
}

class Node {
	public ArrayList<Item> Items;
	public ArrayList<Node> Children = new ArrayList<Node>();
	
	public Node(ArrayList<Item> items) {
		this.Items = items;
	}
}

class Tree {
	public Node Root;
	public Tree() {
		this.Root = new Node();
	}
	public void Build(ArrayList<item> items) {
		ArrayList<Node> nodes = new ArrayList<Node>();
		foreach (Item item in items) {
			ArrayList<Item> items = new ArrayList<item>();
			items.Add(item);
			nodes.Add(new Node(items));
		}
		
		this.Filter(this.Root, nodes);
	}
	
	public void Filter(Node node, ArrayList<Node> candidates) {
		foreach (Node candidate in nodes) {
			if(this.PassCondition(candidate)) {
				node.Children.Add(candidate);
				this.Filter(candidate, this.Permutations(candidates));
			}
		}
	}
	
	public bool PassesCondition(Node node) {
			// check your supports here? do you need any other information other than the single node?
	}
	
	public List<Node> Permutations(Node node, ArrayList<Node> candidates) {
		ArrayList<Node> nodes = new ArrayList<Node>();
		for (int index = candidates.indexOf(node) + 1; index < candidates.Count(); index++) {
			nodes.Add(new Node(node.Items.Union(candidates[index].Items));
		}
	}
}