## 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
You might be experiencing some problems with Your Video player.

# Slides

0:00 Slides Introduction to Algorithms - Lecture 9 Binary-search-tree sort Analysis of BST sort Node depth Expected tree height Height of a randomly built binary search tree Convex functions Convexity lemma with Proof Proof of convexity lemma (1) Proof of convexity lemma (2) Proof of convexity lemma (3) Proof of convexity lemma (4) Jensen's inequality Jensen's inequality - Proof (1) Jensen's inequality - Proof (2) Analysis of BST height (1) Analysis of BST height (2) Exponential height recurrence (1) Exponential height recurrence (2) Exponential height recurrence (3) Exponential height recurrence (4) Exponential height recurrence (5) Solving the recurrence (1) Solving the recurrence (2) Solving the recurrence (3) Solving the recurrence (4) Solving the recurrence (5) The grand finale (1) The grand finale (2) The grand finale (3) The grand finale (4) Post mortem (1) Post mortem (2) Thought exercises

# Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.

# 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..."

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !