22. (4 pts) Which one of the following recurrences is linear and homogeneous? T(n) = 2(n+1)-...
22. (4 pts) Which one of the following recurrences is linear and homogeneous? o T(n) =T(n 2020) + 1 T(n) =T(n+1) - T(m - 2) +T(n – 3) 3 the four other possible answers are incorrect T(n) = 2T(n/2) + 4n ап = am-1 + An-1
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)
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
no coding solve it by hand (2) Homogeneous Linear Recurrences where p(A) has repeated roots (a) Let Let f(n) = an. Show f(n) = d,2n +d2n2" satisfies a(ai)iez be a sequence of real numbers p(A)f(n) (A 2)2(f(n)) 0 for every di, d2 0. . (2) Homogeneous Linear Recurrences where p(A) has repeated roots (a) Let Let f(n) = an. Show f(n) = d,2n +d2n2" satisfies a(ai)iez be a sequence of real numbers p(A)f(n) (A 2)2(f(n)) 0 for every di, d2...
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
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3. recurrenсes T(п) log n n 4T .3 3.1 n 5T 2 n2 log n T(п) 3.2 Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3....
What is the solution to the following recurrence? T(n) = 16T(3/4)+ n T(1) = 1 T(n) = 0n) T(n) = 0 (n1/2) T(n) = O(na) T(n) = O(n log(n)) the four other possible answers are incorrect
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
3. Solve the follwoing recurrences using the master method. (a) T(n) = 4T (n/2) + navn. (8 pt) (b) T(n) = 2T (n/4) + n. (8 pt) (c) T(n) = 7T(n/2) +n?. (8 pt)
Solve the following recurrences using substitution. (n)T(n 2)3n + 4,for all n 2 3. G iven T(1) = 1, and T(2) 6