private void RemoveItem(TwoFourTreeNode node, int index)
{
/*
* To remove a value from the 2–3–4 tree:
* 1. Find the element to be deleted.
* • If the element is not in a leaf node, remember its location and continue searching until a leaf, which will contain the element’s successor, is reached.
* The successor can be either the largest key that is smaller than the one to be removed, or the smallest key that is larger than the one to be removed.
* It is simplest to make adjustments to the tree from the top down such that the leaf node found is not a 2-node. That way, after the swap, there will not be an empty leaf node.
* • If the element is in a 2-node leaf, just make the adjustments below.
* Make the following adjustments when a 2-node – except the root node – is encountered on the way to the leaf we want to remove:
* 1. If a sibling on either side of this node is a 3-node or a 4-node (thus having more than 1 key), perform a rotation with that sibling:
* • The key from the other sibling closest to this node moves up to the parent key that overlooks the two nodes.
* • The parent key moves down to this node to form a 3-node.
* • The child that was originally with the rotated sibling key is now this node's additional child.
* 2. If the parent is a 2-node and the sibling is also a 2-node, combine all three elements to form a new 4-node and shorten the tree. (This rule can only trigger if the parent 2-node is the root,
* since all other 2-nodes along the way will have been modified to not be 2-nodes. This is why "shorten the tree" here preserves balance; this is also an important assumption for the fusion operation.)
* 3. If the parent is a 3-node or a 4-node and all adjacent siblings are 2-nodes, do a fusion operation with the parent and an adjacent sibling:
* • The adjacent sibling and the parent key overlooking the two sibling nodes come together to form a 4-node.
* • Transfer the sibling's children to this node.
* Once the sought value is reached, it can now be placed at the removed entry's location without a problem because we have ensured that the leaf node has more than 1 key.
*/
if (node.IsLeafNode)
{
node.RemoveItem(index);
if (node.KeyNum == 0 && node != _root)
{
Debug.Assert(node.Parent != null);
AdjustNodeWhenRemove(node);
// if (node.GetChildIndex() < 0) node.Invalidate();
}
_count--;
_version++;
}
else
{
var successor = node.Children[index].GetMaxLeafNode();
var item = successor.Items[successor.KeyNum - 1];
node.Items[index] = item;
RemoveItem(successor, successor.KeyNum - 1);
}
}
