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Math Help - Function Growth Rates

  1. #1
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    Function Growth Rates

    Hello I am trying to figure out what is the growth rates for some fucntions.
    So far I only know the order for the basic functions but I would also like to know where would some special/different fucntions would fit


    From textbook:

    Constant, logN, logn^2, N, NlogN, N^2, N^3 and 2^N (right side growing the fastest)



    I would like to know where would the following fucntions fit

    N^(1/2), loglogN, N / logN, (1/3)^N, (3/2)^N

    Here is my guess,

    When N is small such as using N=2

    Constant, loglogN, N, N^(1/2), logn^2, logN, N, NlogN, (1/3)^N, (3/2)^N, N / logN

    When N is a large number such as N=333

    Constant, loglogN, logN, logn^2, NlogN, (1/3)^N, N^(1/2), N, (3/2)^N, N / logN


    A guess with out plugging in numbers for N

    Constant, loglogn, logn, logn^2, n^(1/2), n, nlogn, (1/3)^n, (2/3)^n, n/logn


    This is how I came to my guess, I tried plugging in numbers into N for each fucntion and look at their results. However I got different results of growth order when I used different numbers. I used 2 and 333 for N. Some fucntions grew much faster with a bigger N than with a smaller. I am not sure how to figure out my problem.



    Thanks for your help!
    Last edited by hotmail590; October 4th 2006 at 06:38 PM.
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  2. #2
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    Quote Originally Posted by hotmail590 View Post

    Constant, logN, logn^2, N, NlogN, N^2, N^3 and 2^N (right side growing the fastest)
    I am not sure what your question is.
    Below I have attached a hand drawn graph showing each one except the function 2^n because it starts out slow but then overtakes all of them since I was zoomed in I did not want things to get messy. Yes that order is correct.

    (Just curious are you doing algorithm complexity in discrete math class?)
    Attached Thumbnails Attached Thumbnails Function Growth Rates-picture11.gif  
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  3. #3
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    Sorry for the unclarity in my question. To put it simplily, I would like to know if the ordering of the follow fuctions based on growth rate is correct. I tried using this online function grapher and I'm not sure if my results are correct Function Grapher Online


    here is what I got (had to kinda pasted 2 graphs together since the program only allows up to 5 functions)

    http://www.geocities.com/shini590/graph.bmp


    17
    (1/3)^n
    (3/2)^n
    loglogn
    logn
    n^(1/2)
    log(n)^2
    n/logn
    n
    nlogn <-- grows fastest


    Yes, this question came to me when I was in class today. I am taking a course on algorithm analysis.

    Thanks for your help!
    Last edited by hotmail590; October 4th 2006 at 07:37 PM.
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  4. #4
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    Constant
    loglogn
    logn
    logn^2
    n^(1/2)
    n
    nlogn
    Good
    (1/3)^n
    (2/3)^n
    Usually exponentials are the fastest but in this case these are reciprocal exponentials. I would say that they the slowest in growth. In fact, they have no growth at all!
    n/logn <-- this being the fastest in growth
    How can it be faster than nlog n?
    If n/log n you are dividing by a number larger than unity?


    I am take a course on algorithm analysis.
    Cool
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  5. #5
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    Sorry I edited my previous post a couple times perhaps you replied while I was editing it. I noticed some of my mistakes and reordered them.

    This is my final answer

    (1/3)^n
    (3/2)^n
    17
    loglogn
    logn
    n^(1/2)
    log(n)^2
    n/logn
    n
    nlogn <-- grows fastest

    please check (does't log(n)^2 grow faster than n^(1/2) ?)


    Thank you very much for your help!
    Last edited by hotmail590; October 7th 2006 at 12:21 AM.
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