We have a tree with n(n < 1e5) nodes and we have a constant k(k < 1e5) can we store the k'th ancestor of all nodes in an array or there is no way to do that??? Thank you for helping :)

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We have a tree with n(n < 1e5) nodes and we have a constant k(k < 1e5) can we store the k'th ancestor of all nodes in an array or there is no way to do that??? Thank you for helping :)

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easiest way is binary lifting to kth parent using sparse table (similar to lca).

space complexity:O(nlogn)

Complexity:O(nlogn)

Hi teja349 how can I do the binary search in O(logn)? I already know it in O(logn*logn) because I know the kth parent in O(logn) plus the binary search

let's say that

khas the following binary representation: 0011010This means that you need to climb up (2

^{1}= 2 nodes) + (2^{3}= 8 nodes) + (2^{4}= 16 nodes), the order doesn't matterTo do this you can loop over the bits of

kand if thei^{th}bit set, go up 2^{i}nodesSince we have

O(log_{2}(n)) bits, we go up by a power of two and we doO(1) work on the sparse table, the overall complexity isO(log_{2}(n))You can solve in O(N) by maintaining an explicit dfs stack in a vector as you dfs from the root. From each node you then look at the kth last thing in the vector if it exists.

I think this is actually much easier than using a sparse stable (although sparse tables can be easily extended to non constant k-th ancestor queries)