(а) Т(п) — 2T(п/3) + Ө(nlogn) (b) т(п) — 3т(п/5) +@(log? n) (c) Т(п) — 9T(п/3) + Ө(п?)
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- Give tight asymptotic upper bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for sufficiently small n. Please give me a step by step answers, thanks.Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that each T(n) is a constant for n ≤ 2. Make your bounds as tight as possible, andjustify your answers.Give the solution for T(n) in the following recurrence. Assume that T(n) is constant for small n. Provide brief justification for the answer.
- How many lines will the following function write? Write the recurrence relation of each and solve using the Master theorem. Give your answer as a function of n (in the form Θ( · )).Please explain Give asymptotic upper and lower bounds for each of the following recurrences. Justify your answer. T(n)=√nT(√n)+nQuestion 3 Please solve the recurrence and show its proof by induction of: T(1) = 3 T(n) = T(n/3) + 2n, n > 1
- Find the solution to each of the following recurrence relations, given the initial conditions, i.e., find a formula for an, where n = 0, 1, 2, 3, .... a. a0 = 2; an = −an-1. b. a0 = 2; an = an-1 + 4. c. a0 = 1; an = (n+1)an-1. d. a0 = 4; an = an-1 − n.Prove or disapprove the time complexity guess for each of the following recurrences using the subsitution method. (using induction) T(n) = T(n/2) + 1 is O(logn).Find the order of growth for solutions of the following recurrences using master theorem. 1. T(n) = 4T(n/2) + n, T(1) = 1 2. T(n) = 4T(n/2) + n^2, T(1) = 1 3. T(n) = 4T(n/2) + n^3, T(1) = 1
- Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T (n) is constant for n ≤ 3. Make your bounds as tight as possible, and justify your answers T (n) = 3T (n/5) + log^2 nGive asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T (n) is constant for n ≤ 3. Make your bounds as tight as possible, and justify your answers T(n)=T(n/2)+lgn.Express the solution in big-O terms for the following recurrence relation: T(n) = 2T(n-1)+1; T(0)=1