Sharon Curtis and Shin-Cheng Mu. Calculating a linear-time solution to the densest segment problem. Journal of Functional Programming, Vol. 25, 2015.

[Paper (doi: 10.1017/S095679681500026X)| Supplementary Proofs | Code]

The problem of finding a densest segment of a list is similar to the well-known maximum segment sum problem, but its solution is surprisingly challenging. We give a general specification of such problems, and formally develop a linear-time online solution, using a sliding window style algorithm. The development highlights some elegant properties of densities, involving partitions that are decreasing and all right-skew.