# Lecture12 - CSE 421 Algorithms Richard Anderson Lecture 12...

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CSE 421 Algorithms Richard Anderson Lecture 12 Recurrences and Divide and Conquer

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Divide and Conquer
Recurrence Examples T(n) = 2 T(n/2) + cn O(n log n) T(n) = T(n/2) + cn O(n) More useful facts: – log k n = log 2 n / log 2 k k log n = n log k

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T(n) = aT(n/b) + f(n)
Recursive Matrix Multiplication Multiply 2 x 2 Matrices: | r s | | a b| |e g| | t u| | c d| | f h| r = ae + bf s = ag + bh t = ce + df u = cg + dh A N x N matrix can be viewed as a 2 x 2 matrix with entries that are (N/2) x (N/2) matrices. The recursive matrix multiplication algorithm recursively multiplies the (N/2) x (N/2) matrices and combines them using the equations for multiplying 2 x 2 matrices =

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Recursive Matrix Multiplication How many recursive calls are made at each level? How much work in combining the results? What is the recurrence?
Matrix Multiplication Algorithm? Recurrence:

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## This note was uploaded on 02/25/2012 for the course CSE 421 taught by Professor Richardanderson during the Fall '06 term at University of Washington.

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Lecture12 - CSE 421 Algorithms Richard Anderson Lecture 12...

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