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Summary: 1/19
Analysis of Algorithms
Lecture 6
Max Alekseyev
University of South Carolina
September 8, 2010
2/19
Outline
Divide-and-Conquer
Fast Integer Multiplication
Fast Matrix Multiplication
3/19
Fast Integer Multiplication
Let b, c 0 be integers, represented in binary, with n bits each.
Here, n is assumed to be large, so we cannot assume as we usually
do that b and c can be added, subtracted, or multiplied in
constant time.
We imagine that the b and c are both represented as arrays of n
bits: b = bn-1 · · · b0 and c = cn-1 · · · c0, where the bi and ci are
individual bits (leading 0's are allowed). Thus,
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