Maurice Tutor

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    Argosy University/ Phoniex University/
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Category > Computer Science Posted 19 Sep 2017 My Price 3.00

Euclid"s algorithm

Modify Euclid"s algorithm so that given integers m; n as input, it outputs integers a; b such that am + bn = g = gcd(m; n). This is called the extended Euclid"s algorithm.

(a) Use the LNP to show that if g = gcd(m; n), then there exist a; b such that am + bn = g.

(b) Design Euclid"s extended algorithm, and prove its correctness.

(c) The usual Euclid"s extended algorithm has a running time polynomial  in min{m; n}; show that this is the running time of your algorithm, or modify your algorithm so that it runs in this time.

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Maurice Tutor
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Status NEW Posted 19 Sep 2017 01:09 PM My Price 3.00

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