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...