Question: Use Master's Theorem to find the asymptotic bounds for the following ( 4 points) (a)...
Apply Master's Theorem to give asymptotic bounds for T(n) if possible: Apply Master's Theorem to give asymptotic bounds for T(n) if possible: T(n) = {1 if n = 1 4T{n/2) +n/log n if n > 1
Master Theorem : Use the master theorem to give tight asymptotic bounds for the following recurrences b) ?(?) = 2? ( ?/2 ) + ?(? ^ 2 )
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 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
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 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
1. Theorem 4.1 (Master Theorem). Let a 2 1 and b >1 be constants, let f(n) be a function, and let T(n) be defined on the nonnegative integers by the recurrences T(n)- aT(n/b) + f(n) where we take n/b to be either 1loor(n/b) or ceil(n/b). Then T(n) has the following asymptotic bounds. 1. If f(n) O(n-ss(a)-) for some constant e > 0, then T(n) = e(n(a). 2. If f(n) e(n(a), then T(n)- e(nlot(a) Ig(n)). 3. If f(n)-(n(a)+) for some constant...
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;
Question 6 (20 points) Solve the following recurrences using the Master Theorem. T(n) = 2T (3/4)+1 T(n) = 2T (n/4) + va 7(n) = 2T (n/4) +n T(n) = 2T (3/4) + n
use master's theorem to solve the following recurrence relation T(n) = 8T(n/2) + nlog(n)