Is there a formal methodology for determining time complexity of an implementation of an algorithm?

Question

Basically what the title says. take for example a simple function:

def swap(a,b)
temp = a
  a = b
  b = temp

This one is pretty easy to solve intuitively. if we consider an assignment as a single operation the time complexity T(n) = 3 for any n where n is the input size. But for more complex code e.g. one involving multiple nested loops/ different loop types it will be much harder using an informal approach.

score 2 · Accepted Answer · answered Jun 06 '24 at 21:24

No, not necessarily. The undecidability of the halting problem proves there is no general algorithm that always works for all algorithms/programs.

But see Is there a system behind the magic of algorithm analysis? for a systematic approach that often works for real-world algorithms.

Is there a formal methodology for determining time complexity of an implementation of an algorithm?

1 Answers1