Download Intro to Computer Algorithms Lecture 6

Intro to Computer Algorithms
Lecture 6
Phillip G. Bradford
Computer Science
University of Alabama
Announcements
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Colloquia on Monday 22-Sept
David M. Mount presents:
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“Approximation Algorithms for
Clustering”
At 11:00 in 108 Houser
Lecture Outline
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Homework Assignment
Review last lecture
More on Recurrences
Exhaustive Search
Divide and Conquer
Reading
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Up through Chapter 3
Start Chapter 4.
Exhaustive Search
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Brute-Force String Matching
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Elements in string: n
Elements in search string: m
Closest Point Problems
Traveling Salesperson
Knapsack Problem
More Recurrence Examples
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T(n) = 2T(n/2) + 1
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Solution?
How about
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T(n) = 2T(n/2) + n
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Assume n is a power of 2.
Divide and Conquer
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Divide instance in to parts
Solve problem on the parts
Combine the solutions
The Master Theorem
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T(n) = aT(n/b) + f(n)
M. Theorem. Suppose f(n) is Q(nd) and
d > 0. Then T(n) is
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Q(nd)
if a < bd
Q(nd log n) if a = bd
Q(nlogba)
if a > bd
Examples
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Recall, T(n) = 2T(n/2) + 1
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Here, f(n) = 1 and a = b = 2 and d = 0.
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So, a > bd
Giving: T(n) is Q(nlogba) = Q(n)