Note: this post contains heavy spoilers about Round 1124 1C, 1D and 1E.

On today's round, it appears problems C, D, and E are all related to cartesian trees in one way or another. Specifically:

-Problem C can be solved by doing smaller-to-larger merging('DSU on tree') on the cartesian tree formed by a; While this wasn't the only hard part of the problem, I'd say it was regardless the central observation.

-In problem D, the operation 'move to the first index j > i with p_j > p_i' can easily be interpreted in terms of moving upwards by some amount on the cartesian tree of p. This gives an easy proof that 1) the edges i->j form a forest and 2) any forest can be formed by some array p, allowing one to reduce the problem to tree DP. Although the indices j can be calculated using only a stack, knowledge on cartesian trees still helps one approach the problem.

-The process given in problem E is identical to the process one would use to construct the cartesian tree of a given array in O(n log n) using a segment tree. This immediately gives a bijection between 'Trees of Life' and binary trees, telling us that there are precisely C_n of them(the n-th catalan number), a fact which is very useful in solving the problem.

I'm sure many people solved some or all of these problems without even thinking/knowing about cartesian trees, but it was still interesting to me that three consecutive problems on the same round are related to the same, rather uncommon topic. Maybe this isn't worth writing a blog about, idk.