Big O complexity of inner loops

Question

The Big O of Outer loop is O(n),and I think second inner loop big O is log(n) but I cant't figure the big O of the third inner loop

for(i=0;i<n;i+=2)
{
    for(j=1;j<i*i;j*=3)
    {
       for(k=2;k*k<=n;k++){}
    }
}

Possible duplicate of [Big O for 3 nested loops](https://stackoverflow.com/questions/14510701/big-o-for-3-nested-loops) — , Mar 30 '19 at 14:05

Sandeep Polamuri · Accepted Answer · 2019-03-30T13:49:25.623

0

The outermost loop gets executed n-2 times making the complexity O(n). In the second loop the value of j increases in powers of 3 up to i*i that is equal to log3(i*i). so for both the loops combined, it is ∑ _i=1^n-2 log3(i) which is equal to log3(n!) or simply n*log(n) as you mentioned. The innermost loop gets executed sqrt(n) times making the total complexity O(n*log(n)*sqrt(n))

edited Mar 30 '19 at 13:49

answered Mar 30 '19 at 12:32

Sandeep Polamuri

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Adding an explanation for why you believe that what you're saying is indeed the case would improve this answer quite a lot. – Michael Kenzel Mar 30 '19 at 12:55

Big O complexity of inner loops

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