Master Method
Use the Master Method to give tight Θ bounds for the followingrecurrence relations. Show a, b, and f(n). Then explain whether itfits one of the cases, and if so why while choosing ε, c, and n0where necessary. Write and simplify the final Θ result.
(a) T(n) = 2T(n/4) + √n
(b) T(n) = 3T(n/9) + n3
(c) T(n) = 7T(n/3) + n
Substitution
Use substitution as directed below to solve
T(n) = 7T(n/3) + n
(a) First, use the result from the MasterMethod in (c) above as your “guess” and inductive assumption. (Whenremoving Θ, just use one constant c rather than c1 and c2.) Takethe proof
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