Question

I need to implement a step function (i.e. piecewise constant). There are a few requirements that it will need to have.

1. It will have to be evaluated repeatedly at random locations, then evaluated sequentially over an interval.
2. It Will have to be easily updated, i.e. adding an increase/decrease over an interval.

So my question is what is the best data structure for this sort of thing? I was thinking that due to the random access nature a Binary tree is the most likely, but I’m hoping I’m not missing something. Also is there a good implementation already out there for C++.

Answer 1

Yes, since the intervals cannot overlap, binary tree is the right data structure. If you did not need fast updates, it could be as simple as having a sorted sequence of the interval endpoints; querying the function value at a certain location could be done using, for example, one of the STL binary search methods std::lower_bound or std::upper_bound, evaluating over a range using two searches. However, for fast updates a self-balancing binary tree is naturally better.

The standard library does define a container with tree-like access: std::map (although it is not required to be implemented using a binary tree, it usually is).

for completeness, it should be mentioned that Boost ICL library has an interval_map, a std::map-like container that uses intervals as keys and with aggregate on overlap insertion semantics.