MIT 6.046J / 18.410J Introduction to Algorithms - Fall 2005

Lecture 9: Relation of BSTs to Quicksort, Analysis of Random BST

author: Erik Demaine, Center for Future Civic Media
recorded by: Massachusetts Institute of Technology, MIT
published: Feb. 10, 2009, recorded: October 2005, views: 3516
released under terms of: CC BY-NC-SA

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Slides

Slides
0:00	Introduction to Algorithms - Lecture 9
0:12	Binary-search-tree sort
6:02	Analysis of BST sort
18:56	Node depth
23:01	Expected tree height
26:21	Height of a randomly built binary search tree
32:24	Convex functions
37:06	Convexity lemma with Proof
40:36	Proof of convexity lemma (1)
43:10	Proof of convexity lemma (2)
45:29	Proof of convexity lemma (3)
46:21	Proof of convexity lemma (4)
46:47	Jensen's inequality
50:40	Jensen's inequality - Proof (1)
51:45	Jensen's inequality - Proof (2)
55:45	Analysis of BST height (1)
63:25	Analysis of BST height (2)
65:29	Exponential height recurrence (1)
66:42	Exponential height recurrence (2)
67:15	Exponential height recurrence (3)
69:38	Exponential height recurrence (4)
71:29	Exponential height recurrence (5)
72:09	Solving the recurrence (1)
73:49	Solving the recurrence (2)
75:10	Solving the recurrence (3)
76:17	Solving the recurrence (4)
76:29	Solving the recurrence (5)
77:48	The grand finale (1)
77:51	The grand finale (2)
77:54	The grand finale (3)
77:57	The grand finale (4)
79:29	Post mortem (1)
79:56	Post mortem (2)
80:47	Thought exercises

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Description

"So, we're going to talk today about binary search trees. It's something called randomly built binary search trees. And, I'll abbreviate binary search trees as BST's throughout the lecture. And, you of all seen binary search trees in one place or another, in particular, recitation on Friday. So, we're going to build up the basic ideas presented there, and talk about how to randomize them, and make them good. So, you know that there are good binary search trees, which are relatively balanced, something like this. The height is log n..."