Consider the recurrence T (n) = T (⌈n/4⌉) + T (⌈n/3⌉) + n with T (1)...

Question

Question

Consider the recurrence T (n) = T (⌈n/4⌉) + T (⌈n/3⌉) + n with T (1) = 1.

12 points

(a) (4 Points) Using a recursion tree, determine a tight asymptotic upper bound on T(n).
(b) (4 Points) Prove your upper bound using induction.
(c) (4 Points) Using a suitable variable change, solve the recurrence U (n) = 3U (⌈n^(1/3) ⌉) + 7 with U(2) = 1.

engineering Computer-Science

Answer 1

Answer #1

Answer 2

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