How to judge the relative efficiency of algorithms given runtimes as functions of 'n'?

Posted by Lopa on Stack Overflow See other posts from Stack Overflow or by Lopa
Published on 2010-03-23T17:11:19Z Indexed on 2010/03/26 5:33 UTC
Read the original article Hit count: 388

Filed under:

algorithm

|

homework

Consider two algorithms A and B which solve the same problem, and have time complexities (in terms of the number of elementary operations they perform) given respectively by

a(n) = 9n+6

b(n) = 2(n^2)+1

(i) Which algorithm is the best asymptotically?

(ii) Which is the best for small input sizes n, and for what values of n is this the case? (You may assume where necessary that n>0.)

i think its 9n+6. guys could you please help me with whether its right or wrong?? and whats the answer for part b. what exactly do they want?

© Stack Overflow or respective owner

Related posts about algorithm

Jpeg Algorithm vs BMP Algorithm?

as seen on Super User - Search for 'Super User'
I'm just wonder, what the differences are between creating a BMP file algorithm and JPG file algorithm ? If you know the others images' format algorithm, please post them. Thanks. >>> More
word disambiguation algorithm (Lesk algorithm)

as seen on Stack Overflow - Search for 'Stack Overflow'
Hii.. Can anybody help me to find an algorithm in Java code to find synonyms of a search word based on the context and I want to implement the algorithm with WordNet database. For example, "I am running a Java program". From the context, I want to find the synonyms for the word "running", but the… >>> More
Search algorithm (with a sort algorithm already implemented)

as seen on Stack Overflow - Search for 'Stack Overflow'
Hello, Im doing a Java application and Im facing some doubts in which concerns performance. I have a PriorityQueue which guarantees me the element removed is the one with greater priority. That PriorityQueue has instances of class Event (which implements Comparable interface). Each Event is associated… >>> More
Is there any algorithm for finding LINES by PIXEL COLORS on picture?

as seen on Stack Overflow - Search for 'Stack Overflow'
So I have Image like this I want to get something like this (I hevent drawn all lines I want but I hope you can get my idea) I need algorithm for finding all straight lines on it by just reading colors of pixels. No hard math, no Haar, no Hough. Some algorithm which would be based on points… >>> More
collsion issues with quadtree [on hold]

as seen on Game Development - Search for 'Game Development'
So i implemented a Quad tree in Java for my 2D game and everything works fine except for when i run my collision detection algorithm, which checks if a object has hit another object and which side it hit.My problem is 80% of the time the collision algorithm works but sometimes the objects just go… >>> More

Related posts about homework

parsing a list and producing a structure of that

as seen on Stack Overflow - Search for 'Stack Overflow'
;; structure representing homework points ;; nr: number - the number of the homework ;; points: number - the number of points reached (define-struct homework (nr points)) ;; parse-homework: (list of number pairs) -> (list of homework) ;; The procedure takes a list of number pairs and produces… >>> More
Scheme homework help

as seen on Stack Overflow - Search for 'Stack Overflow'
Okay so I have started a new language in class. We are learning Scheme and i'm not sure on how to do it. When I say learning a new language, I mean thrown a homework and told to figure it out. A couple of them have got me stumped. My first problem is: Write a Scheme function that returns true (the… >>> More
Unix [Homework]: Get a list of /home/user/ directories in /etc/passwd

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm very new to Unix, and currently taking a class learning the basics of the system and its commands. I'm looking for a single command line to list off all of the user home directories in alphabetical order from the /etc/passwd directory. This applies only to the home directories, and not the contents… >>> More
sequential search homework question

as seen on Stack Overflow - Search for 'Stack Overflow'
Consider a disk file containing 100 records a. How many comparisons would be required on the average to find a record using sequential search, if the record is known to be in the file? I figured out that this is 100/2 = 50. b. If the record has a 68% probability of being in the file, how many comparisons… >>> More
[Homework] Online programming editor

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi, For a school project i need to write or use a online programming editor. It is a part of a bigger project. I thought of a java application, php/html/javascript or flash. I have a couple of things i could do: Find a good working application and edit it so it works with the rest of the project Find… >>> More