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COMP 731 - Data Struc & Algorithms - Lecture 7 - Thursday, July 6, 2000
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Today:
Solving recurrence relations
More on Divide-and-conquer and divide-and-conquer recurrences
* State the Master Theorem
* Do some examples where the master theorem does and does not apply
* Do some examples of further recurrence relations, like
T(n) = n T(n-1)
T(n) = 3 + T(n-1)
* Binary search and it's recurrence relations
* Multiplication
- using the grade-school algorithm, and its analysis (Theta(n^2))
- using the 4-multiply-(n/2)-bit numbers method, and its analysis (Theta(n^2))
- using the 3-multiply-(n/2)-bit numbers method, and its analysis
(Theta(n^\lg 3)) \subseteq Theta(n^1.59)
* State best known bound for this problem