Root out the roots
Given a perfect binary tree of depth , how many nodes exist such that the tree could be rerooted there such that the resulting tree is still a binary tree (but not necessarily perfect)?
Clarification:
- You know all nodes and their corresponding values and their connections; but you don't know which node is root, parent or child or leaf if any. Depth of a tree with only one node is .
- A fully-connected binary tree is that whose nodes have either two or no children.
- A perfect binary tree is a fully connected binary tree in which all leaves are at the same level.
The problem is a part of this set
The answer is 1025.
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