O(n^2) vs O (n(logn)^2)

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悲哀的现实
悲哀的现实 2021-02-01 23:18

Is time complexity O(n^2) or O (n(logn)^2) better?

I know that when we simplify it, it becomes

O(n) vs O((logn)^2)
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  •  Happy的楠姐
    2021-02-01 23:27

    (logn)^2 is also < n.

    Take an example:

     n = 5
     log n = 0.6989....
     (log n)^ 2 = 0.4885..
    

    You can see, (long n)^2 is further reduced.

    Even if you take any bigger value of n e.g. 100,000,000 , then

       log n = 9
       (log n)^ 2 = 81
    

    which is far less than n.

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