whatsapp

Connect on Whatsapp : +97143393999, Uninterrupted Access, 24x7 Availability, 100% Confidential. Connect Now

Securing Higher Grades Costing Your Pocket? Book Your Assignment at The Lowest Price Now!
loader
Add File

Error goes here

Files Missing!

Please upload all relevant files for quick & complete assistance.

Guaranteed Higher Grade!

CP5602 Advanced Algorithm Analysis

tag 0 Download 6 Pages / 1,434 Words tag 19-02-2021
  • Course Code: CP5602
  • University: James Cook University
    icon

    MyAssignmentHelp.com is not sponsored or endorsed by this college or university

  • Country: Australia

Question:

Aim: This assignment is designed to evaluate/improve your critical thinking and problem solving skills. It also evaluate/improve your coding skill.

  1. For a tree T, let nI denote the number of its internal nodes, and let nE denote the number of its external nodes. Show that if every internal node in T has exactly 3 children, then nE = 2nI + 1. [2 marks]
  2. Suppose we are given two ordered search tables S and T, each with n elements (with S and T being implemented with arrays). Describe an O(lg2n)-time algorithm for finding the kth smallest key in the union of the keys from S and T (assuming no duplicates).
  3. Although merge sort runs in (n lg n) worst-case time and insertion sort runs in (n2 ) worst case time, the constant factors in insertion sort make it faster for small n. Thus, it makes sense to use insertion sort within merge sort when sub problems become sufficiently small. Consider a modification to merge sort in which n/k sub lists of length k are sorted using insertion sort and then merged using the standard merging mechanism, where k is a value to be determined.
  4. i) Show that the n/k sub lists, each of length k, can be sorted by insertion sort in (nk) worst-case time. [1 mark]
  5. ii) Show that the sub lists can be merged in (n lg(n/k)) worst-case time. [2 marks]

Given that the modified algorithm runs in (nk + n lg(n/k)) worst-case time, what is the largest asymptotic (notation) value of k as a function of n for which the modified algorithm has the same asymptotic running time as standard merge sort. [3 marks]

Consider the recurrence T(n) = 3T(⌊n/2⌋) + n.
 
i) Use the master method to give tight asymptotic bound for this recurrence (if the master method cannot be used, explain why).
 
ii) Use a recursion tree to determine a good asymptotic upper bound on this recurrence. [2 marks]

iii) Use the substitution method to verify your answer. [1 mark]

When an adjacency-matrix representation is used, most graph algorithms require time ?(V2 ), but there are some exceptions. Show that determining whether a directed graph G contains a universal sink (i.e. a vertex with in-degree |V | − 1 and out-degree 0) can be determined in time O(V ), given an adjacency matrix for G. [5 marks]<span style="mso-spacerun:'yes';font-family:Arial;mso-fareast-font-family:'Times New Roman'; mso-bidi-font-family:'Ti
Download Sample Now

Earn back the money you have spent on the downloaded sample by uploading a unique assignment/study material/research material you have. After we assess the authenticity of the uploaded content, you will get 100% money back in your wallet within 7 days.

Upload
Unique Document

Document
Under Evaluation

Get Money
into Your Wallet

Total 6 pages

Cite This Work

To export a reference to this article please select a referencing stye below:

My Assignment Help (2021) Advanced Algorithm Analysis [Online]. Available from: https://myassignmenthelp.com/free-samples/cp5602-advanced-algorithm-analysis/optimization-algorithms-for-networks.html
[Accessed 19 August 2022].

My Assignment Help. 'Advanced Algorithm Analysis' (My Assignment Help, 2021) <https://myassignmenthelp.com/free-samples/cp5602-advanced-algorithm-analysis/optimization-algorithms-for-networks.html> accessed 19 August 2022.

My Assignment Help. Advanced Algorithm Analysis [Internet]. My Assignment Help. 2021 [cited 19 August 2022]. Available from: https://myassignmenthelp.com/free-samples/cp5602-advanced-algorithm-analysis/optimization-algorithms-for-networks.html.


We Can Help!

Get top notch assistance from our best tutors !
Excel in your academics & career in one easy click!

icon

Other Samples

Content Removal Request

If you are the original writer of this content and no longer wish to have your work published on Myassignmenthelp.com then please raise the content removal request.

icon

5% Cashback

On APP - grab it while it lasts!

Download app now (or) Scan the QR code

*Offer eligible for first 3 orders ordered through app!

screener
ribbon
callback request mobile
Have any Query?