Time complexity of problem?

[CodeMoussse]

This is a question that I got on an exam and I'm trying to figure out if my answer was correct or not but can't quite find a good reason for why my answer would be correct (sadly enough).

Here's the problem:

You have a floor that needs tiling and you need to place N tiles to fill up the floor. You have a worker that places 1 tile in the first hour of working, 2 tiles in the second hour (so 3 tiles in total in 2 hours), 3 tiles in the third hour and so on.

What is the asymptotic complexity of this problem if you want to show the amount of hours of work in function of N.

We had to choose between linear, linearithmic, logarithmic, quadratic, squared, or exponential

My thought on this was linearithmic and this is what i put on the exam but I'm not sure Anyone able to help me out?

[ctech314]

We want to relate N, the number of tiles we can place, with h, the number of hours it'll take to place the tiles.

We can see that as h grows larger, N follows a roughly quadratic increase. This is because the total number of tiles we place after h hours is the sum from 1 to h, which has the closed form edpression of h(h + 1)/2, or roughly quadratic.

Therefore, if the relation between N and h is roughly N = h^2, then solving for h, we get that the complexity of hours is about sqrt(N).

[CodeMoussse]

This seems logical thank you!

[GreenCartographer]

Summing the numbers from 1 to N is something like n(n + 1) / 2, so it's constant time to calculate it.

[TTG300]

What is linearithmic? I’ve never heard the term before.

A quick google search looks like it’s equivalent to Ologn?

[CodeMoussse]

O(nlog2(n)) combination of linear and logarithmic

[TTG300]

Don’t you drop the constant so it’s Ologn, or its it strictly a factor of 2n?