COP 3503 Computer Science II Fall 2005 Week Eight

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COP 3503 - Computer Science II (Fall 2005) Week
Eight

• By Yunjun Zhang

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AVL tree

• Named after its discoverers, Adelson-Velskii and
  Landis)
• It is a BST with balance conditions.
• Depth log(N)
• Definition
• BST
• For any node in the tree, the difference between
  the height of left subtree and right subtree is
  at most 1

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AVL tree

• Properties
• An AVL tree of height H has at least FH3-1
  nodes, where Fi is the ith Fibonacci number.
• Proof on board.

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AVL tree

• Ideas behind AVL tree
• Balance conditions are violated when insertion or
  deletion operate.
• Rotations must be performed to maintain the
  balance condition.
• Single/Double rotation. Symmetric for left or
  right version.

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AVL tree

• Insertion
• Single Rotation
• Double Rotation
• On board

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AVL tree

• Deletion
• Delete the node as in a binary search tree.
• The node deleted will be either a leaf or have
  just one subtree.