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Maximum Rule

  1. Apr 2, 2008 #1
    please help me to prove that:
    O(max(f1(n),f2(n),......,fk(n))) = O(f1(n) + f2(n) + .... + fk(n))

    thank you
  2. jcsd
  3. Apr 2, 2008 #2


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    Proof by induction looks like the obvious thing to try.
  4. Apr 2, 2008 #3
    what O meens???

    there is some logical error
    weird flying robot question

    in the first part you mention:
    i can only guess that the max function returns the maximal value
    among the presented functions
    on the other hand you say that this maximal value should be equaled to the sum
    of all the presented functions in the list.
    i think that the only way i t could work
    is when all the functions except one are all zeros
    you have f1=0 f2=0 ..f15=50 f16=0 etc..
    then their sum also equals to the maximal function value.
    this whole thing is only a presumption

    well i am back to my digital design questions
    Last edited: Apr 2, 2008
  5. Apr 2, 2008 #4


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    If you do not understand a notation, just ask about it and assume that what other people are saying is wrong!

    The "O" notation refers to the "order" or, for functions of an integer, n, the rate of convergence (or divergence) as n goes to infinity. Saying that O(max(f1(n), f2(n),..)= O(f1(n)+ f2(n)+ ...) says that the sequence formed by choosing ai the largest of f1(i), f2(i), ..., converges (or diverges) as fast as the sequence an= sum of f1(n)+ f2(n)+ ....
  6. Apr 2, 2008 #5
    'O' is the 'Big Oh' notation in complexity theory.

    HallsofIvy, you're right the proof is by induction.
    I've used the fact that f1(n)+....+fk(n) <= k*max(f1(n),.....,fk(n)) (proved by induction also), am I on the right route ?
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