The-Winner's blog

Minimum/maximum distance between coprime nodes
By The-Winner, 18 months ago, In English

I was wondering if there is any faster algorithm than O(N^2) that solves the following problem: Given a tree made of N nodes, where each node has an integer value asociated to it, find the minimum/maximum distance between two nodes whose values are coprime(if such a pair exists).

For example, given the following tree:

The minimum distance is 1 and can be obtained in multiple ways, but one of them is:

And the maximum distance is 4 and can be obtained like this:

I couldn't find anything like this by googling so I thought this is the best place to ask. Thank you in advance.

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18 months ago, # |
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What's the constraint for ai

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    18 months ago, # ^ |
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    I didn't find this problem anywhere, just thought about it, I suppose you can make it <=N or <=1e6 or 1e7.

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18 months ago, # |
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Deleted.

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18 months ago, # |
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It can be solved using centroid decomposition but I'm not aware of the details

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18 months ago, # |
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By using centroid decomposition you can turn the problem into finding $$$b_i = \max_{i\perp j} a_j$$$, which can be solved by using parallel binary search in $$$O(n \log n 2^{\omega(n)})$$$.The whole complexity is $$$O(n \log^2 n 2^{\omega(n)})$$$.

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    18 months ago, # ^ |
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    How are you using parallel binary search if there are no queries ?

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      18 months ago, # ^ |
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      Each $$$b_i$$$ is a query.

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