BST Search Time

• Includes, LowerBound, Upperbound, Insert, Put, Get, Erase
1. Dominated by BST Search
2. Runtime is O(h), where h = height of tree
• How does h related to n = size of tree?
• From basic theory: log n <= h < n
• Worst Cases (h = n - 1)
1. Insert items in sorted order
2. Insert items in reverse sorted order
• Best Cases (h = log n) - Insert in "level order"
• Random Case
1. Theorem: If items are inserted in random order, h = O(log n)
2. Problem: World is often not random. Data tends to be ordered, or mostly ordered

?? Need better BST algorithms ??