Suppose we're given a string of $n$ positive numbers and asked to split it into the maximum number of substrings whose totals are decreasing. I have an $O(n)$ time DP algorithm, but is it already known? I can find lots of pages about splitting the numbers into the maximum number of subsets (or, more precisely, sub-multisets) with decreasing sums --- to build a pyramid, for example --- but I don't want to rearrange the numbers.
For example, given $6, 2, 4, 3, 2, 2, 5$, we can split it into $6, 2, 4$ (total $12$) and $3, 2, 2$ (total $7 < 12$) and $5$ (total $5 < 7$).
This started as an open problem at CCCG '21. Here's a detailed presentation: https://arxiv.org/abs/2109.14497 .