- The problem is designed to be solved using a segment tree. This is a data structure that comes up in competitive programming, but isn’t covered in the standard algorithms textbooks (e.g., Sedgewick or CLRS). So I studied it for the first time in preparation for solving this problem.
- A static segment tree like the one described in Wikipedia, is not sufficient. Solving this problem requires a segment tree that implements lazy propagation so that updates can be made efficiently.
- As an extra challenge, the problem author added the requirement for an “invert” operation. This adds some implementation complexity and means a generic segment tree implementation won’t work.
- Java solutions seem to run very close to the time limit, which is a generous five seconds for this problem. Even an efficient solution that addresses the previous points may nevertheless need some additional performance tweaking to run fast enough.
Read on for solutions to these issues, and an explanation of how to go about coding a solution.