Prove that the size of an instance will always decrease at least by a factor of 2 after two successive iterations of Euclid's algorithm.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter18: Deterministic Dynamic Programming
Section: Chapter Questions
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5. Algorithm analysis (Ex.5.6-1)
a. If we measure the size of an instance of the problem of computing the great-
est common divisor of m and n by the size of the second parameter n, by
how much can the size decrease after one iteration of Euclid's algorithm?
b. Prove that the size of an instance will always decrease at least by a factor
of 2 after two successive iterations of Euclid's algorithm.
Transcribed Image Text:5. Algorithm analysis (Ex.5.6-1) a. If we measure the size of an instance of the problem of computing the great- est common divisor of m and n by the size of the second parameter n, by how much can the size decrease after one iteration of Euclid's algorithm? b. Prove that the size of an instance will always decrease at least by a factor of 2 after two successive iterations of Euclid's algorithm.
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