Solve the following recurrences by repeatedly unrolling them, aka the method of substitution. You must show...
(12 pts) Solve each of the following Do not only state your solution- Show how you obtained it. That is, if you use substitution, you must present the complete inductive proof that your solution is correct. If you obtained the solution from the tree. Note that you are to prove matching upper and lower bounds recurrences using substitution or a recursion tree. use a recursion tree, show the recursion tree and discuss how you (а) Т(п) — 4T (п/2) +...
Part A Analyze the following recurrences and show their time complexity functions using (I) iteration method and (2) Master Theorem. AI. T(n) = 2T 3 A2. T(n) = 3T 2n АЗ. Т(п) — Т(п — 2) + 3 А4. Т(п) — 2Т (п — 1) + 1 A5. T(n)= 4T +n log n A6. T(n) = 3T +n log n n2 A7. T(n) = 27 Part B Do 2.3-4 (р39) and Problem 2-1 (р39) Part C Implement MERGE-SORT() algorithm that...
Problem 2 Solve the following recurrences. You only need to obtain the asymptotic solution (in e) notation). If you use the master theorem, you must specify all parameters and briefly verify all conditions. 1. (5%) T(n) = 25T(F) + n2 +n, T(1) = 5.