We have a variable n which sets granularity.

level of granularity, would be 12,500 less than that.

So we lose a little bit of granularity of information.

Experiments show that it's best to stick with a granularity you once have achieved, because then you won't have to track back through all the levels of granularity you already have seen.

We simply keep on working with these new reduced, simplified inputs and a decreased granularity.

You don't necessarily know with granularity exactly what organisms are providing what flavors and what characteristics.

We define the length of the individual subset by simply dividing the length of the entire input by occurring granularity.

We now need to increase the granularity but must make sure it doesn't get over the length of the total string.

Neither removal of these subsets would fail, so now we have to increase the granularity by coming up with now four subsets.

And most granularly, I break them down by religion where there are 72 categories of religions in the world so an extreme level of granularity.

Removing any of these subsets will result in a passing test, which means that we again have to increase the granularity by doubling n in here.

The point is just that understanding tiny constant factors in the analysis is an inappropriate level of granularity for the kind of algorithm analysis we're going to be doing in this course.

Now we split the input into six subsets, resulting in six more attempts to remove individual parts all of them will pass and then we have to increase the granularity again, which would be 12.

We decrease the granularity by 1 but don't let it fall below 2, and we set the variable some complement is failing to true, because we need this to step out of this loop, which we do right away.

We split the input into initially two subsets, and if any of these subsets fails, as in here, we proceed with this very subset, otherwise, we simply go and increase the granularity, that is, we double the number of subsets and we go again to step one.

The second guiding principal is we're not going to focus on constant factors or lower returns, that would be inappropriate, given the level of granularity at which we're describing algorithms and third is where going to focus on the rate of growth of algorithms for large problem sizes.

What we do in this situation is we increase the granularity, that is, we take away smaller parts more frequently until we end up removing single characters such that we really, really get an input where every single character or every single part is relevant for reproducing the failure.