1. Assume that T(1)=1, if no base case is given. (a) Solve using the iteration method: T(n) = 2 T(n/2) + 1, for n > 1.
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Given: T(n) = 2 T(n/2) + 1 For n = 2: T(2) = 2 T(2/2) + 1 = 2 T(1) + 1 = 2(1) + 1 = 3 For n = 4: T(4) = 2 T(4/2) + 1 = 2 T(2) + 1 = 2(3) + 1 = 7 For n = 8: T(8) = 2 T(8/2) + 1 = 2 T(4) + 1 = 2(7) + 1 = 15 From the Show more…
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