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Index 1 and the value of the root are not the same. Binary tree root can contain any value. That part of the problem declaration is ambiguous. For example:
/ \ / \
10 6 9 17
Is still a binary tree. It's not sorted, but that does not disqualify it as a binary tree.
The problem says "You are given a tree of n nodes where nodes are indexed from 1..n and it is rooted at 1. " So we can safely assume that the binary tree we will be given for this problem always has a root of 1. I dealt with this by creating a BinaryTree object with a root of 1.