Intro to Computer Algorithms Lecture 11

Phillip G. BradfordComputer Science

University of Alabama

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Outline

Go over HW 4 More Divide-and-Conquer &

Analysis Exam Review

First Midterm Exam

I expect a good deal of preparation by my class

Thursday 9-October Closed Book & Closed Notes Start with your home works Text book Notes

The week of 6-Oct

I will be in Taiwan and Hong Kong doing research

Prof. Borie will give Lectures in my absence!

Back to the Closest Pair Problem

N points, then (N choose 2) pairs Compute the distance between

each possible pair and Find the minimum of this list of O(N2)

distances Total cost: O(N2) Can we do better?

The Closest Pair Problem

How about divide-and-conquer on the x-coordinate? Then the y-coordinate? What’s wrong with this?

Splitting the set gives a large cost for re-merging

Sort by x-coordinate and recursively by y-coordinate

The Closest Pair Problem

d1

d2

d d

The Closest Pair Problem

The 6 points principle

P

d

d

d

d

The Closest Pair Problem

Cost? O(N log N) per dimension T(N) = 2T(N/2) + cN Master Theorem: T(N) = O(N log

N).

Exam Review Solving Recurrences

Unwinding: Formality expected by induction

Master Theorem: give a, b and d. Designing & Analyzing Exhaustive

Sear or Brute Force Algorithms Designing & Analyzing Divide and

Conquer Algorithms