Define the gcd function for more than two arguments by the recursive equation gcd (a 0 ,
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Define the gcd function for more than two arguments by the recursive equation gcd (a0, a1, . . . ,an) = gcd (a0, gcd (a1, a2, . . . ,an). Show that the gcd function returns the same answer independent of the order in which its arguments are specified. Also show how to find integers x0, x1, . . . ,xn such that gcd (a0, a1, . . . ,an) = a0x0 + a1x1 + ···+ anxn. Show that the number of divisions performed by your algorithm is O(n + lg(max {a0, a1, . . . ,an})).
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Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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