broly_1033's blog

Path Queries 2 on CSES
By broly_1033, history, 17 months ago, In English

Hi everyone, I was studying how to solve query problems on trees using Euler Tour. I was wondering how to solve path query problems on trees. We can solve problems which can be solved by maintaining a prefix array (for e.g. sum of nodes in path from a to b), but how to solve say, node with maximum value in path from a to b. Can anyone guide me on this?
More specifically, sum(a, b) = sum(root, a) + sum(root, b) — 2*sum(root, lca(a, b)) + val(lca). I was using this to solve these problems using Euler Tour. But I cannot find maximum using this (CSES Path Queries 2).
Q1. Can we apply segment trees on Euler Tour array? Q2. How to solve problems like CSES Path Queries 2?

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17 months ago, # |
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Yah you need to use heavy light decomposition, which basically uses segment tree.

I hope this helps

https://codeforces.com/blog/entry/81317

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    17 months ago, # ^ |
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    I have heard of HLD but couldn't seem to grasp it. Thanks, is there any other method though?

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      17 months ago, # ^ |
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      It is a fairly high level concept, if I was you I would focus on easier topics first.

      No I don't think there's any other way of solving this problem.

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7 weeks ago, # |
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My O(Nlog^2N) code is TLEing in the last test, any idea why ?

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    3 days ago, # ^ |
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    Hey! I saw your code, eventhough it is asymtotically optimal, there are few optimizations you could do. 1. You are accumulating ranges in a vector and querying the segment tree later. Instead directly query the segment tree. Avoid the intermediate list overhead. 2. This is not needed:
    if (par != -1) { node.leg.erase(find(node.leg.begin(), node.leg.end(), par)); node.depth = 1 + T[par].depth; } 3. Try doing minor optimizations here and there.

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