Algorithmic complexity of naive code for processing all consecutive subsequences of a list: n^2 or n^3?

Question

I\'m studying for a test and found this question:

I can\'t really determine the complexity, I figured it\'s either O(n²) or O(n³) and I\'m lea

Answer 1

You can model the running time of the function as

sum(sum(sum(Theta(1), k=i+1..j),j=i..n),i=1..n)

As

sum(sum(sum(1, k=i+1..j),j=i..n),i=1..n) = 1/6 n^3  - 1/6 n,

the running time is Theta(n^3).