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Course: Numerical Optimization
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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.