The big theorem
effect of rotations mysterious, subtle and actually not that well understood.
Splay Tree Theorem:
- Any sequence of m dictionary operations on a splay tree that is initially empty and never has more than n modes uses O(m log n) time in worst case. Therefore, the operations have amortized O(log n) time.
Analysis subtle: need to show that time “saved” while performing low-cost operations can be “saved up for use” during time-consuming operations
We’ll spend the next several slides proving this.