hello codeforces, I have been trying to learn about splay trees from this.In the analysis of alternate implementations insertion and deletion it has been mentioned that this follows from a modification of the proof of lemma 1(Access lemma).

I could find proofs for this when all weights are taken as 1 for example here

but i could'nt find one for the general weighted case nor can prove it myself. so can anyone please help ? thanks!

no one has been able to solve this problem and the editorial is not clear. could anyone please give a better explanation. i.e what is the state of the dp ? and how to move from one state to another ?

problem name : "therectangularcitydiv1" problem link: https://community.topcoder.com/stat?c=problem_statement&pm=14901&rd=17158

editorial: https://www.topcoder.com/blog/single-round-match-734-editorials/