For each of the following recurrence relations, determine the runtime T(n) complexity. Use the Master Theorem to solve the recurrence relations if the recurrence relations can be solved using Master Theorem, otherwise use expansion (or recursive substitution) to solve the recurrence relations. You must show all your working to justify your answer. Solution without clear justification or steps scores no mark. (a) T(n) = 4T () + n² + n (b) (). T(n) = = 16T +n

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For each of the following recurrence relations, determine the runtime T(n)
complexity. Use the Master Theorem to solve the recurrence relations if the
recurrence relations can be solved using Master Theorem, otherwise use
expansion (or recursive substitution) to solve the recurrence relations. You must
show all your working to justify your answer. Solution without clear justification
or steps scores no mark.
(a)
T(n) = 4T (4) + n² + n
(b)
T(n) = 16T (A + n
(c)
T(n) = 16T (2) + n³
(d)
T(n) = T(n – 1) + nª
(e)
T(n) = 2T () + n lg n
Transcribed Image Text:For each of the following recurrence relations, determine the runtime T(n) complexity. Use the Master Theorem to solve the recurrence relations if the recurrence relations can be solved using Master Theorem, otherwise use expansion (or recursive substitution) to solve the recurrence relations. You must show all your working to justify your answer. Solution without clear justification or steps scores no mark. (a) T(n) = 4T (4) + n² + n (b) T(n) = 16T (A + n (c) T(n) = 16T (2) + n³ (d) T(n) = T(n – 1) + nª (e) T(n) = 2T () + n lg n
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