Question

Solve the following recurrences: (a) T(n) = T(n=2) + O(n), with T(1) = 1. Solve this...

Solve the following recurrences:
(a) T(n) = T(n=2) + O(n), with T(1) = 1.
Solve this two times: one with the substitution method and one with the master theorem from
CLRS. When you use the master theorem, carefully show the values for the parameters a; b.
For the following cases you can use your preferred method. In either case, show your work:
(b) T(n) = 2T(n/2) + O(1), T(1) = 1.
(c) T(n) = 3T(n/2) + O(1), T(1) = 1.
(d) T(n) = T(2n/3) + O(1), T(1) = 1.
(e) T(n) = T( √n) + O(1); T(2) = 1.
Note: In all the above examples you should give T(n) in O-notation.

Engineering   Computer-Science   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use Master Theorem to solve the following recurrences. Justify your answers. (1) T(n) = 3T(n/3) +...
Use Master Theorem to solve the following recurrences. Justify your answers. (1) T(n) = 3T(n/3) + n (2) T(n) = 8T(n/2) + n^2 (3) T(n) = 27T(n/3) + n^5 (4) T(n) = 25T(n/5) + 5n^2
Master Theorem: Let T(n) = aT(n/b) + f(n) for some constants a ≥ 1, b >...
Master Theorem: Let T(n) = aT(n/b) + f(n) for some constants a ≥ 1, b > 1. (1). If f(n) = O(n logb a− ) for some constant > 0, then T(n) = Θ(n logb a ). (2). If f(n) = Θ(n logb a ), then T(n) = Θ(n logb a log n). (3). If f(n) = Ω(n logb a+ ) for some constant > 0, and af(n/b) ≤ cf(n) for some constant c < 1, for all large n,...
Solve the recurrence relation using the substitution method: 1. T(n) = T(n/2) + 2n, T(1) =...
Solve the recurrence relation using the substitution method: 1. T(n) = T(n/2) + 2n, T(1) = 1, n is a 2’s power 2. T(n) = 2T(n/2) + n^2, T(1) = 1, n is a 2’s power
Solve the following recurrences  using the recursion tree method T(n) = 4 T(n/4) + n, where T(1)...
Solve the following recurrences  using the recursion tree method T(n) = 4 T(n/4) + n, where T(1) = 0
Suppose T(n) is defined recursively as: T(0) = 1 T(n) = 3T(n-3) + O(n) True or...
Suppose T(n) is defined recursively as: T(0) = 1 T(n) = 3T(n-3) + O(n) True or false: T(n) ∈ O(2n)
Q1. What are the theta values for the recurrences given below in : (1) T(n) =...
Q1. What are the theta values for the recurrences given below in : (1) T(n) = T((8/10)n) + n (2) T(n)=5T(n/5) + n^2 (3) T(n) = T(n-2) +2n
Given T(n)= T(n-1) + 2*n, using the substitution method prove that its big O for T(n)...
Given T(n)= T(n-1) + 2*n, using the substitution method prove that its big O for T(n) is O(n^2). 1. You must provide full proof. 2. Determine the value or the range of C.
topic is Algorithms, where you see O it means big O.please solve and explain Is 2^(n+1)...
topic is Algorithms, where you see O it means big O.please solve and explain Is 2^(n+1) = O(2^(2n)) ? Is 2^(2n) = O(2^n)?
Does the Master theorem apply to the following recurrences. Justify your answer in each case. If...
Does the Master theorem apply to the following recurrences. Justify your answer in each case. If it applies, then also state the case and the solution. (a) T(n) = √ nT(n/2)+logn, (b) T(n) = T(n/2+ 31)+log n, (c) T(n) = T(n−1)+T(n/2)+n and (d) T(n) = T(n/7)+T(5n/13)+n.
Solve the following recurrence relations. If possible, use the Master Theorem. If the Master Theorem is...
Solve the following recurrence relations. If possible, use the Master Theorem. If the Master Theorem is not possible, explain why not and solve it using another approach (substitution with n = 3h or h - log3(n). a. T(n) = 7 * n2 + 11 * T(n/3) b. T(n) = 4 * n3 * log(n) + 27 * T(n/3)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT