Andersson Trees

• Every tree keeps track of the left-level; that is, the number of hops to the sentinel when considering only the left children.
  • All sentinel nodes have a left-level of zero.
  • All leaf nodes (nodes with no children) have a left-level of one.
• The left rule: The left-level of a tree must always be the left-level of its left child plus one.
• The right rule: The left-level of a tree may be the same as the left-level of its right child. However, it must be greater than the left-level of its right grandchild.
• After an insertion into the tree:
  • Check to see if the left rule is violated. If so, perform a right rotation.
  • Check to see if the right rule is violated. If so, perform a left rotation.
  • When performing rotations, update the levels of the rotated nodes whenever a node acquires a new left node. Its new level will be the level of the new left node, plus one.
• Make sure that the invariant restoration is performed after every insertion, including the recursive calls.

Removing a node

• If the difference between the level of a parent and either of its children is greater than one, reduce the level of the parent by one.
• If this subtraction makes the level of the right child greater than the level of its parent, set the level of the right child to the level of its parent.
• Enforce the left rule on the parent, its right child, and its right grandchild, in that order.
• Then enforce the right rule on the parent and its right child, in that order.