Harvard University Lower Bounds and Linear Time Sorting Questionnaire


3 attachmentsSlide 1 of 3attachment_1attachment_1attachment_2attachment_2attachment_3attachment_3

Unformatted Attachment Preview

Question 6: Lower Bounds and Linear time Sorting
• (a) A set of n natural numbers are uniformly distributed in the range 1 < x < Vn. Determine the runtime (in big-Theta notation) of Counting Sort and Radix Sort. Find the expected runtime of Bucket sort using 10 buckets. Which algorithm has the best asymptotic runtime? (b) Given a set of three numbers {a,b,c} draw the comparison-based decision tree that represents the execution of bubble-sort. Justify the length of the longest-path in your tree, using the results of problem 5 from practice set 1. 4 Figure for problem lc: Below shows one step of the girls sorting process. Examining bears 5 and 1, she decides they need to be swapped. Then she moves left and will examine bears 4 and 1 next. Problem 5: You may have already come across another simple sorting algorithm called Bubble-sort. Instead of describing the algorithm here, you are asked to do a bit of online research. One great place to start is here: https://www.youtube.com/watch?v=lyZQP JUT5B4 Write the basic pseudo-code for Bubble sort, using comparisons and swaps. Determine the worst-case number of swaps and the worst-case number of comparisons. Repeat for the best-case. Problem 5 Assume that the input to Bubble sort is an array A indexed from 1 to n. The algorithm below passes through the elements of the array and swaps any two adjacent elements that are not in relative order. The process continues until a full pass can be made without any swaps. made-swap = true while(made-swap) made-swap = false for i = 1 to n-1 if A[i+1] < A[i] Swap A[i] and A[i+1] made-swap = true Worst-case: Note that in the above algorithm, each execution of the for-loop carries out exactly n-1 comparisons. If the array is sorted in reverse order, then after each pass of Bubblesort the maximum element of the unsorted section is moved into the last position. For example, starting with 5, 4, 3, 2, 1 after one pass of bubble-sort the array becomes: 4,3,2,1,5, and after the second pass the array becomes 3, 2, 1,4,5. Each pass places exactly one element in its final sorted position, and therefore n passes are needed. Each pass performs exactly n 1 comparisons, and therefore the worst-case number of comparisons is n(n-1). The number of swaps made during the first pass is n-1, during the second is n-2, etc. Therefore the total number of swaps is n(n-1)/2 in the worst case. Best-case: Bubblesort is effective if it is given an array that is already sorted. It is able to detect this right away, and return the sorted array after one pass. This is because on a sorted array, 1, 2, 3, 4, 5, Bubblesort performs no swaps on the first pass, and therefore will not repeat a second pass. Therefore the best-case number of swaps is 0 and the best-case number of comparisons is n - 1. Purchase answer to see full attachment Tags: algorithms lower bounds inear time Sorting User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Looking for this assignment?

do my essay homework

Reviews, comments, and love from our customers and community

Article Writing

Great service so far. Keep doing what you do, I am really impressed by the work done.



PowerPoint Presentation

I am speechless…WoW! Thank you so much! Definitely, the writer is talented person. She provided me with an essay a day early before the due date!

Stacy V.

Part-time student

Dissertation & Thesis

This was a very well-written paper. Great work fast. I was in pretty desperate need for help to finish this paper before the due date, which was in nine hours.

M.H.H. Tony


Annotated Bibliography

I love working with this company. You always go above and beyond and exceed my expectations every time. Kate did a WONDERFUL job. I would highly recommend her.

Francisca N.


Book Report / Review

I received my order wayyyyyyy sooner than I expected. Couldn’t ask for more. Very good at communicating & fast at replying. And change & corrections she put in the effort to go back and change it!

Mary J.


Essay (Any Type)

On time, perfect paper. All concerns & matters I had Tom was able to answer them! I will definitely provide him with more orders!

Prof. Kate (Ph.D)


Case Study

Awesome! Great papers, and early! Thank you so much once again! Definitely recommend to trust James with your assignments! He won’t disappoint!

Kaylin Green


Proofreading & Editing

Thank you Dr. Rebecca for editing my essays! She completed my task literally in 3 hours. For sure will work with her again, she is great and follows all instructions

Rebecca L.


Critical Thinking / Review

Extremely thorough summary, understanding and examples found for social science readings, with edits made as needed and on time. It’s like having a tutoring service available (:

Arnold W.



Perfect!I only paid about $80, which i think was a good price considering what my paper entailed. My paper was done early and it was well written!

Joshua W.


Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>