Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Computer Science Posted 17 Sep 2017 My Price 4.00

Euclid"s algorithm

Analysis of bit operations in Euclid"s algorithm

a. Consider the ordinary "paper and pencil" algorithm for long division: dividing a by b, which yields a quotient q and remainder r. Show that this method requires O((1 + lg q) lg b) bit operations.

b. Define μ(a, b) = (1 + lg a)(1 + lg b). Show that the number of bit operations performed by EUCLID in reducing the problem of computing gcd(a, b) to that of computing gcd(b, a mod b) is at most c(μ(a, b) - μ(b, a mod b)) for some sufficiently large constant c > 0.

c. Show that EUCLID(a, b) requires O(μ(a, b)) bit operations in general and O(β2) bit operations when applied to two β-bit inputs.

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Maurice Tutor
(5)
Status NEW Posted 17 Sep 2017 09:09 AM My Price 4.00

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