logarithmic complexity represented with loop?

Question

as far as I got it linear complexity can be represented as simple loop and quadratic complexity can be represented as nested loop. How can the cubic and logarithmic complexity be represented?

Thanks!

Answer 1

A simple loop can have logarithmic complexity, e.g.

for (i = 1; i <= N; i *= 2)
    ...

As others have already answered, a triple nested loop will have cubic complexity.

Answer 2

Since cubic is O(n^3), it would be three nested loops.

Logarithmic is not so straightforward and usually requires a recursive relation. For example, MergeSort is O(n*log(n)) because it forms a recursion tree of height log(n) and each level requires an O(n) merging operation.