[algorithm] How to find the lowest common ancestor of two nodes in any binary tree?

Well, this kind of depends how your Binary Tree is structured. Presumably you have some way of finding the desired leaf node given the root of the tree - simply apply that to both values until the branches you choose diverge.

If you don't have a way to find the desired leaf given the root, then your only solution - both in normal operation and to find the last common node - is a brute-force search of the tree.

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How to find the lowest common ancestor of two nodes in any binary tree?