Optimal greedy algorithm for Interval Partitioning requires computing the depth of the instance before it can assign labels to each request. In fact, it is possible to solve the problem without having to compute the depth in advance. Modify the algorithm so that it does not need to know the depth before assigning labels. Why the modified algorithm is still correct.

And note how the modified algorithm implicitly computes the depth since the number of resources used in the resulting schedule is equal to the depth of the instance.