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What is the time complexity of the following recursive function

int DoSomething(int n){
     if(n<=2) 
        return 1;
     else 
        return (DoSomething(floor(sqrt( n) )) + n);
}

Options are:-

  1. O(n^2)
  2. O(n log n) //all logs are with base 2
  3. O(log n )
  4. O(log log n )
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  • as it is, this is a bad question. this is clearly a homework problem and you have not demonstrated any effort to solve it on your own. not that you likely care, but here's how to ask a question Commented Jun 29, 2017 at 6:36
  • Well, this is not a homework problem, this was on GATE 2007 paper. Commented Jun 30, 2017 at 6:28

1 Answer 1

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The time complexity function is (ignoring floor as it is asymptotically irrelevant):

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We need to find m when the algorithm terminates, i.e. when:

enter image description here

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