Question: Task: Use a recursion tree to determine a good asymptomatic upper bound on the recurrence T(n) = 3T(n/2) + n. Use the substitution method to

Task: Use a recursion tree to determine a good asymptomatic upper bound on the recurrence T(n) = 3T(n/2) + n. Use the substitution method to verify your answer.

Solution:

Task: Use a recursion tree to determine a good asymptomatic upper bound

Could you please explain step by step what is going on in this problem? What is required to find, and why do we substitute a particular condition into the equation? Why they have T(n[n/2]) instead of just T(n)? How did we get 3cn^(lg(3))/2^lg(3) - 3n + n?

Since in a recursion tree, the depth of the tree will be lg(n), and the number of nodes that are i levels below the root is 3i. This means that we would estimate that the runtime is i=0lg(n)3i(n/2i)=ni=0lg(n)(3/2)i=n.5(3/2)lg(n)1nlg(3). We can see this by performing a substutiton T(n)cnlg(3)2n. Then, we have that T(n)=3T(nn/2)+n3cnlg(3)/2lg(3)3n+n=cnlg(3)n So, we have that T(n)O(nlg(3))

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T (n) = 3T (n/2) + n. Use the substitution method to verify your answer.

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T (n) = 4T (n/2 + 2) + n. Use the substitution method to verify your answer.

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T ( n ) = 4 T ( n / 2 + 2 ) + n . Use the substitution method to verify your answer. ( pls do it in step by step and...

2) (8 points, 4 points each): We used Recursion Trees (CLRS Section 4.4) to figure out the runtime for MergeSort (Slide 13 of Lecture 5), to figure out runtime for two multiplication algorithms...

a. Use a recursion tree to determine a good asymptotic upper bound on the recurrence T .n/ D 3T .bn=2c/ C n. b. Use the substitution method to verify your answer.

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T (n) = T (n 1) + T (n/2) + n. Use the substitution method to verify your answer.

please solve this Question 40 points Implement such and solutions to the following problem faciting poufix exprentices informing fireprosto por experi We are providing emple code drie public...

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T ( n ) = T ( n /2) + n 2 . Use the substitution method to verify your answer.

using recursion tree to determine a good asympotic upper bound on the recurrence T(n) = 4T(n/2) + n2 Use the substitution method to verify your answer

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T (n) = 2T (n 1) + 1. Use the substitution method to verify your answer.

Complete the reaction Na2Co3+2HCl 2NaCl+H2O + {fill_regular}.

A 8 % , 1 0 year, $ 1 0 0 0 bond with semiannual payment provides a YTM of 9 % . what is the current Yield on this bond? 8 % 8 . 5 6 % 9 % None of the above

Father Williams received the Form W - 2 below. He incurred $ 3 , 0 0 0 of unreimbursed expenses connected with his ministerial earnings: $ 2 , 5 0 0 related to his ministerial salary. $ 5 0 0 related...

15-14 What would your company need to do to create a successful e-commerce presence in China? Explain.

15-12 Describe the political, cultural, and organizational obstacles for foreign companies that want to do business online in China.

15-10 In this project youll use the web to research overseas distributors and customs regulations and use Internet-based software to calculate prices in foreign currencies. You are in charge of...