Question

How would you find a T(n) run-time (not the big O run time) for a function that has two inputs? Do you just consider the a input your ‘n’?

int h(int a, int b) {
  if (a > 0) {
    return h(a-1, a+b);
  } 
  else {
    return 0;
  }
}

Answer 1

In this case we just need to consider a since the length of this algorithm isn’t dependent on b.

In other words since we can pass in 20000 or -2 for b and not impact our time in the slightest (ignoring the actual time of adding a+b) we shouldn’t have to consider b in our calculations.

In a more general case, if the input did depend on a and b we would simply account for this in our time complexity function. In other words it would be T(a, b) not just T(a).