1) a)Show that the algorithm of the Russian peasant for integer multiplication takes (n^2) time in...

   

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1) a)Show that the algorithm of the Russian peasant for integer multiplication takes (n^2) time in the worst case, where n is the total number of digits in the input. b)We saw that the runtime for Mergesort complies with the following recurrence: T (n) = 2T (n/2) + n, with T (1) = 1. Show with induction (at k) that value to T(n) = 2^(k) *T (n / 2^(k)) + kn for positive integer k. 1) a)Show that the algorithm of the Russian peasant for integer multiplication takes (n^2) time in the worst case, where n is the total number of digits in the input. b)We saw that the runtime for Mergesort complies with the following recurrence: T (n) = 2T (n/2) + n, with T (1) = 1. Show with induction (at k) that value to T(n) = 2^(k) *T (n / 2^(k)) + kn for positive integer k.

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Heres how to solve the problem using induction Base Case T1 1 This is because multiplying a singledi... View the full answer