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Question

You are given a binary tree in a peculiar string representation. Each node is written in the form (lr), where l corresponds to the left child and r corresponds to the right child.

If either l or r is null, it will be represented as a zero. Otherwise, it will be represented by a new (lr) pair.

Here are a few examples:

• A root node with no children: (00)
• A root node with two children: ((00)(00))
• An unbalanced tree with three consecutive left children: ((((00)0)0)0)

Given this representation, determine the depth of the tree.