Question

I’m just studying for my data structures & algorithms final. The following question was on my midterm and I got it wrong, so I’m just trying to figure it out:

What is the complexity of the following pseudocode?

 x <- 0
 for x <- 0 to n:
   for y <- 0 to n:
     y <- y + 1
     y <- y * 2

On the midterm I answered O( n^2 ) but now that I’m looking at it again, I think it might be O( nlogn ).. See my answer below showing my attempt.

What is the correct answer?

Any help is helping me pass my exam!

Cheers!

Answer 1

The following is my answer for the moment…

The outer loop for x <- 0 to n executes n times, definitely.

The inner loop for y <- 0 to n appears to execute n times, however every time it executes, its contained code brings y exponentially closer to n. So I believe that this section of code executes with O( logn ) complexity.

Thus, the whole algorithm executes with O( nlogn ) time complexity.