The first two recurrences are clearly not linear.
And the fourth one is logarithmic and the last one looks like quadratic.
So all four given options look incorrect.
Hence the correct answer is the third option - the four other possible answers are incorrect.
22. (4 pts) Which one of the following recurrences is linear and homogeneous? o T(n) =T(n...
22. (4 pts) Which one of the following recurrences is linear and homogeneous? T(n) = 2(n+1)- T(m - 2)+T(– 3) An = an-1 + an-1 T(n) = 2T(n/2) + 4n () T(n) =T(m - 2020)+1 the four other possible answers are incorrect
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
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
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
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 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;
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
4. (20 points) For each of the following recurrences, give an expression for the runtime T(n) if the recurrence can be solved with the Master Theorem. Otherwise, explain why the Master Theorem does not apply. Justify your answer (1) T(n) = 3n T(n) + n3 (2) T(n)-STC)VIOn* (3 Tn)T)+ n logn (4) T(n) T(n-1) + 2rn (5) T(n) 16TG)+n2