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Another summation problem

  1. Nov 30, 2004 #1
    Hello, I really trying to understand what is going on with these summations.
    the code is following:
    Code (Text):

    for p = 2 to n
        for i = 1 to n - p + 1
            j = i + p -1
            for k = i to j - 1
               O(1) + O(1)
    Does j enter anywhere here besides the upper bound of the inner-most summation?
    Here is what I have so far
    Code (Text):

        n     n-p+1    j-1
      Sigma  Sigma    Sigma(C) = Sigma  (C) Sigma (j-1-i) = ...
       p=2    i=1      k=i

    then I break up the double sums on sums of j, -1, and i.
    In the course of my attempt to solve this thing, I cannot get rid of j, while the expression is supposed to be in terms of n.
    How do I get around it?

    Thanks a lot.
  2. jcsd
  3. Dec 1, 2004 #2


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  4. Dec 1, 2004 #3
    Even with that, I still have j and cannot get rid of it!!!
  5. Dec 1, 2004 #4


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    You have [tex]\sum_{p=2}^{n}\sum_{i=1}^{n-p+1}\sum_{k=i}^{j-1}C[/tex] right?

    Stick in j=i+p-1, which is assigned before your 3rd loop, and you get:


    No more j.
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