AVL Trees Splay Trees

Roadmap

Balanced structures

AVL Tree

An AVL Tree Example

Balancing and Logarithms

Maintaining a Balance

Detecting Unbalanced Trees

Repair Method

Single rotation

S.R. Restructuring

Double rotation

D.R. Restructuring

Restructuring

Restructing cont'd

Restructuring summary

Insertion in an AVL

AVL Implementation

AVL Implementation

AVL Insertion Analysis

Removal from an AVL

Splay Tree

Splaying

Zig-Zig Splaying

Zig-Zag Splaying

Zig Splaying

Insertion

Insertion

Analysis

Amortized analysis

Amortized Analysis

Amortization Key

Amortization for Splay Trees

Proving the Amortized Cost

Real Cost

Savings Variation

Zig-zig Proof

Zig-zig Proof cont'd

Zig-zag & Zig Proofs

Wrapping Up the proof

What is Left...