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

COP 3503 - Computer Science II (Fall 2005) Week Eight. By Yunjun Zhang. AVL tree. Named after its discoverers, Adelson-Velskii and Landis) It is a BST with balance conditions. Depth log(N) Definition BST

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

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  1. COP 3503 - Computer Science II (Fall 2005)Week Eight By Yunjun Zhang

  2. 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

  3. AVL tree • Properties • An AVL tree of height H has at least FH+3-1 nodes, where Fi is the ith Fibonacci number. • Proof : on board.

  4. 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.

  5. AVL tree • Insertion • Single Rotation • Double Rotation • On board

  6. 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.

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