sak3t's blog

How to solve this tree problem?
By sak3t, history, 6 years ago, In English

Given a weighted tree of $$$N <= 10^5$$$ nodes, answer $$$Q <= 10^5$$$ queries.
Each query will have $$$node, k$$$ asking number of all the nodes having even weight in the subtree of $$$node$$$ and at a distance $$$k$$$ from $$$node$$$.
Please provide hints.

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6 years ago, # |
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who have weight nodes or edges ? where is the problem ?

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    6 years ago, # ^ |
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    Weights are on nodes.
    Problem is how to compute queries.

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6 years ago, # |
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This problem can be solved offline with a tree technique called DSU on tree

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    6 years ago, # ^ |
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    Can you please briefly explain how it would work?

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6 years ago, # |
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You can do a DFS, maintaining in time and out time. Also maintain a list of nodes for each level in the order in which they appear during the DFS. Each query is finding number of weights in level (k + lev[node]) with DFS in-time in the range [in[node], out[node]]. This can be done in O(logn) using Binary search.

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6 years ago, # |
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If that is another simpler solution since you only need to have the time of entry of each node in the DFS and the time of exit. But my idea is: since the solution for an X node is going to depend on the solution for all the nodes adjacent to X that are not its father, of course, and the nodes that are at a distance K from the X node are the same to say the number of nodes that meet the condition of parity at a depth = lv (x) + k we can take a map for example to keep the solution for a depth Y in the X subtree. Then we only need to join the solution of all the nodes adjacent to X as the solution of X and since the problem can be done offline we can find all the solutions as we calculate the solutions for each node.

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6 years ago, # |
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I think it's about dsu on tree https://codeforces.me/blog/entry/44351

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6 years ago, # |
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If you have to answer queries online then this can be done using persistent segment tree also with time complexity(Q*log(N) + N*log(N).

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