Lecture06-divideconquer

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CS 312: Algorithm Analysis Lecture #6: Divide and Conquer This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick

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Announcements § Project #1 § Due: today (5pm) § HW #4 due Friday § Project #2 § Guidelines and software distribution available from the schedule § We do have one bug fix to release later today, though § Help session on Thursday § §
Objectives § Introduce Divide and Conquer § Apply to Multiplication § Analyze by defining a recurrence relation § Introduce the Convex Hull problem

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Thought “Nothing is particularly hard if you divide it into small jobs.” -- Henry Ford
Divide and Conquer ... Solve the smaller pieces.

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Recall Efficiency of Multiplication Algorithms § Problem: Multiplication § Algorithms: § American § British § a la Francaise / Russe § Arabic § § Efficiency so far:
Recall Efficiency of Multiplication Algorithms § Problem: Multiplication § Algorithms: § American § British § a la Francaise / Russe § Arabic § § Efficiency so far:

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Divide and Conquer 0502 5001 05  50 shift 4 = 250 0000 05  01 shift 2 = 5 00 02  50 shift 2 = 100 00 02  01 shift 0 = 2 2510502
Divide and Conquer 0502 5001 05  50 shift 4 = 250 0000 05  01 shift 2 = 5 00 02  50 shift 2 = 100 00 02  01 shift 0 = 2 2510502 Is it correct?

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0502 5001 05 x 50 shift 4 = 250 0000 05 x 01 shift 2 = 5 00 02 x 50 shift 2 = 100 00 02 x 01 shift 0 = 2 2510502 5001 x 502 10002 0 2500500 2510502 Is it correct? How long does it take on an input of size n?
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