4 (25 marks) A certain algorithm has running time T(n) on input of size n given by T(n) nblg nc 2n 2 blg nc 1 (a) Prove that T(n) is (n log n) (b) Prove that T(n) n lg n is O(n) (c) Explain why the limit rule could not be used for (b) Hint Let L(n) lg n blg nc and think about the properties of the function L For example, how large can it be, and what values does it take when n 1, 2,

The Answer is in the image, click to view ...

Question: 4. (25 marks) A certain algorithm has running time T(n) on input of size n given by T(n) = nblg nc + 2n 2 blg

4. (25 marks) A certain algorithm has running time T(n) on input of size n given by T(n) = nblg nc + 2n 2 blg nc+1 .

(a) Prove that T(n) is (n log n).

(b) Prove that T(n) n lg n is O(n).

Hint: Let L(n) := lg n blg nc and think about the properties of the function L. For example, how large can it be, and what values does it take when n = 1, 2, . . . ?

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!

(25 marks) A certain algorithm has running time T(n) on input of size n given by T(n) = nblg nc + 2n 2 blg nc+1 . (a) Prove that T(n) is (n log n). (b) Prove that T(n) n lg n is O(n). (c) Explain why...

4. (25 marks) A certain algorithm has running time T(n) on input of size n given by T (n) = n Lign+ 2n-211g n+1 (a) Prove that T (n) is (n log n). (b) Prove that T(n) -nlgn is O(n) (c) Explain why...

A full proof would be helpful! Thank you 3. [14 marks] Graph algorithm. Let G-(V. E) be a graph, and let V-{0, 1,.. . , n-1} be the vertices of the graph. One common way to represent graphs in a...

I want to know how to do with these three questions, Problem 2. (10 marks) Consider the following recursive version of InsertionSort: procedure InsertionSort( A, n ) **Sorts array A of size n if n >...

1. The two Java functions below each return a string of length N whose characters are all x. Determine the order of growth of the running time of each, e.g., log N, N, N log N, N^2, N^3, or 2^N. Give...

1. At most, how many comparisons are required to search a sorted vector of 1023 elements using the binary search algorithm? (a) 10 (b) 8 (c) 7 (d) 9 2. The right array in the partition algorithm of...

My main issue is understanding what this assignment is asking me to do and then how to start the project. 5 Interfacing with Blackbox #include #include 2 3 4 5 int main(void) { As a part of this...

Question 1 (5 Marks): All items are equally weighted . 1. At most, how many comparisons are required to search a sorted vector of 1023 elements using the binary search algorithm? (a) 10 (b) 8 (c) 7...

Shopping Spree: (20 points) Acme Super Store is having a contest to give away shopping sprees to lucky families. If a family wins a shopping spree each person in the family can take any items in the...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Proctor compaction test in the laboratory on a borrow pit soil gives a maximum dry unit weight of 19 kN/m3 and optimum water content of 11.5%. The bulk unit weight and water content of the soil in...

Suppose you started a new company, which is expected to generate a Return on Invested Capital ROIC of 15% per year. The company is all-equity financed and the book value of the Invested Capital...

Comcast cable company wants Mickey to buy the full gamut of entertainment products, and the more he buy - digtal television, premium channels, downioadable movies, local and long - distance phone...

CT Corp Comprehensive Question Canadian Tire Corporation, Limited (Canadian Tire) is a family of companies that includes a retail segment and a financial services division, among others. The retail...

(Appendices) During the 20072009 recession, debate in the U.S. Senate over an extension of unemployment benefits to workers who had exhausted their benefits was often heated and contentious. A...

(Appendices) Courtney, age 22, is a junior at a large midwestern university. In late March, she filed applications for summer jobs with three companies. However, she does not want to start work until...

(Appendices) Some states have second-injury funds in their workers compensation programs. However, in recent years, a number of states have terminated such funds.LO6 a. How does a second-injury fund...