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In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child.

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A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well.