Related to : Complexity of enum.values()

What's the order of complexity (Big O) of this code 
The inner loop is O(N^2) for prime numbers but fast for nonprimes
(worst case O(N^1/2) because you only have to search up to sqrt(N)).
The number of prime numbers, however, is small compared to the number
of nonprimes. An approximation of the number of primes to up X is:
X / log(X), as found in this reference link.
So throwing out the nonprimes as inconsequential, there are N /
log(N) prime

Complexity of a basic algorithm? 
When determining complexities, we don't include constants or
coefficients. Instead of O(2N + 2), it should be O(n). We only care
about numbers if they're exponential, i.e. 2^n or n^2, log2(n), etc.
Putting that aside, are you sure this is O(n)? O(n) would mean that it
runs n times, but it looks like j is going to catch up to n before n
times. See what I'm saying?
EDIT: Ok, here's what's going o

SPARQL Query Computational Complexity 
SPARQL itself is PSPACEcomplete. You can probably only come up with
the best case complexity for any given query. The realworld
complexity will depend on the implementation of the database to some
degree.

Heap Sort Space Complexity 
The implementation of heapsort that you've described above sure
doesn't look like it works in constant space for precisely the reason
that you're worried about.
However, that doesn't mean that it's not possible to implement
heapsort in O(1) auxiliary space. Typically, an implementation of
heapsort would reorder the elements in the array to implicitly store a
binary maxheap. One nifty detail abou

Problems regarding calculation of time complexity of a code 
first, you have convince yourself, the problem is bounded by n and the
growth of s.
let see how fast s grows. every iteration, the current value of i will
be added and i itself will add 1. that is, in the jth iteration,
i==j.
so, given any iteration, the current value of s is summing up from 1
to current i, which is roughly i^2, which will be compared to n.
therefore, the number of iterations,
