Using the Master Method give asymptotic bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n ≤ 4.
(a) T(n) = 4 T(n/4) + n lg2 n
(b) T(n) = 3 T(n/4) + n lg n
c) T(n) = 4 T(n/5) + √?
(d) T(n) = 4 T(n/2) + n2 lg n
Using the Master Method give asymptotic bounds for T(n) in each of the following recurrences. Assume...
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. 5.a T(n) = 2T(n/3) + n lg n 5.b T(n) = 7T(n/2) + n3 5.c T(n) = 3T(n/5) + lg2 n
Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n≤2. Make your bounds as tight as possible, and justify your answer. *Hint : You can use Master method to obtain Θ(.). (a) T(n) = 4T(n/4) + 5n (b) T(n) = 4T(n/5) + 5n (c) T(n) = 5T(n/4) + 4n (d) T(n) = 25T(n/5) + n^2 (e) T(n) = 4T(n/5) + lg n (f) T(n) = 4T(n/5) + lg^5 n...
Give asymptotic upper and lower bounds for T(n)in each of the following recurrences. Assume that T(n)is constant forn≤10. Make your bounds as tight as possible, and justify your answers. 1.T(n)=3T(n/5) +lg^2(n) 2.T(n)=T(n^.5)+Θ(lglgn) 3.T(n)=T(n/2+n^.5)+√6046 4.T(n) =T(n/5)+T(4n/5) +Θ(n)
Problem 1 Use the master method to give tight asymptotic bounds for the following recurrences. a) T(n) = T(2n/3) +1 b) T(n) = 2T("/2) +n4 c) T(n) = T(71/10) +n d) T(n) = 57(n/2) + n2 e) T(n) = 7T(1/2) + 12 f) T(n) = 27(1/4) + Vn g) T(n) = T(n − 2) +n h) T(n) = 27T(n/3) + n° lgn
Give asymptotic upper bounds (in terms of O) for T(n) in each of the following recurrences. Assume that T(n) is constant for n < 2. Make your bounds as tight as posible. a) T(n)=T(H) +1; b) T(n) = T(n-1) + 1/n;
Give the asymptotic bounds for T(n) in each of the following recurrences. Make your bounds as tight as possible and justify your answers. Assume the base cases T(0)=1 and/or T(1) = 1. 1. T(n) = T(n-1) + 2n 2. T(n) = T(n-2) = 3
Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for sufficiently small n. Make your bounds as tight as possible, and justify your answers. T(n)=3T(n/3−2)+n/2
Master Theorem : Use the master theorem to give tight asymptotic bounds for the following recurrences b) ?(?) = 2? ( ?/2 ) + ?(? ^ 2 )
Give asymptotic upper and lower bounds for T(n). T(n) is constant for small n. Use either substitution, iteration, or the master method. 1) T(n) = T(n-5) + n 2) T(n) = 2T(n/4) + 16T(n/8) + T(n/8) + 19
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the solution using big-O notation. Explain your reasoning. If the “master theorem” does not apply to a recurrence, show your reasoning, but you need not give a solution. (a) T(n) = 3T(n/2) + n lg n; (b) T(n) = 9T(3/3) + (n? / 1g n); (c) T(n) = T([n/41) +T([n/4])+ Vn; (d) T(n) = 4T([n/7])+ n.