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Is there general pseudocode or related data structure to get the nth value of a b-tree? For example, the eighth value of this tree is 13 [1,4,9,9,11,11,12,13].

If I have some values sorted in a b-tree, I would like to find the nth value without having to go through the entire tree. Is there a better structure for this problem? The data order could update anytime.

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Jonathan
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You are looking for order statistics tree. The idea of it, is in addition to any data stored in nodes - also store the size of the subtree in the node, and keep them updated in insertions and deletions.

Since you are "touching" O(logn) nodes for each insert/delete operation - keeping it up to date still keeps the O(logn) behavior of these.

FindKth() is then done by eliminating subtrees that their bigger index is still smaller than k, and checking the next one. Since you don't need to go to the depth of each subtree, only directly to the required one (and checking the nodes in the path to this element) - you need to "touch" O(logn) nodes, which makes this operation O(logn) as well.

amit
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