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    You're not really asking about a data structure, but about an algorithm: "How do I cache cumulative values stored in a tree?" As it stands, I can't see why the obvious "whenever you change a relevant value in a node, update all its ancestors" strategy wouldn't work. Commented Jan 10, 2019 at 11:13
  • @KilianFoth You're right, my bad. Thank you very much for formulating a question - it yields better google searches than mine :) Commented Jan 10, 2019 at 11:16