AVL Tree Example (This is the example we did in tutorial on Thursday) Slides by Jagoda Walny CPSC 335, Tutorial 02 Winter 2008.

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Presentation transcript:

AVL Tree Example (This is the example we did in tutorial on Thursday) Slides by Jagoda Walny CPSC 335, Tutorial 02 Winter 2008

-1 if the depth of the node’s left subtree is 1 more than the depth of the right node’s left sub tree +1 if the depth of the node’s left sub tree is 1 more than the depth of the right node’s left subtree 0 if both of the node’s subtrees has the same depths -2 if the depth of the node’s left subtree is 2 more than the depth of the right node’s left sub tree +2 if the depth of the node’s left sub tree is 2 more than the depth of the right node’s left subtree If the balance factor becomes -2 or +2, the tree must be rebalanced. Next: Rotations --> AVL trees are self-balancing binary search trees. Each node of an AVL tree is assigned a balance factor as follows:

If the balance factor of a node in an AVL tree is +2 or -2, the node is rotated to rebalance the tree using one of the four cases shown in the following picture: The 4 cases of AVL tree rebalancing using rotations. Picture created by Marc Tanti, licensed for reuse under the GNU Free Documentation License, Version 1.2 Next: example -->

Initial AVL tree with balance factors: Next step: insert 1 --> Balance ok

Insert 1 and recalculate balance factors Next step: Find rebalancing case --> Balance not ok (Balance factor of -2 is not allowed)

Find rebalancing case Next step: apply Left Left rebalancing --> Balance not ok Left Left Case Pivot

Rebalance and recalculate balance factors Next step: insert 30 --> Balance ok

Insert 30 and recalculate balance factors Next step: Insert 32 --> Balance ok

Insert 32 and recalculate balance factors Next step: Find rebalancing case --> Balance not ok

Find rebalancing case Next step: Rebalance (Step 1) --> Balance not ok Left Right Case

Rebalance (Step 1) Next step: Rebalance (Step 2) --> Balance not ok

Rebalance (Step 2) and recalculate balance factors Next step: Insert 35 --> Balance ok

Insert 35 and recalculate balance factors Next step: Find rebalancing case --> Balance not ok

Insert 35 Next step: Rebalance (Step 1) --> Balance not ok Left Right Case Start from first spot (from bottom of tree) where balance factor is incorrect.

Rebalance (Step 1) Next step: Rebalance (Step 2) --> Balance not ok

Rebalance (Step 2) Next step: Finished! --> Balance ok

Finished! Balance ok Exercise: insert 36