Find the Maximum Depth of a Binary Tree

Find the maximum depth of a binary tree. The depth is the number of nodes on the longest path from the root to a leaf. ### Function Contract Implement `maximum_tree_depth(children) -> int`. For a portable interface, `children` is an array of pairs. Node identifiers are `0` through `n - 1`, and `children[i] = [left, right]` gives node `i`'s left and right child identifiers. A missing child is encoded as `-1`. If the tree is nonempty, node `0` is the root. ### Constraints and Clarifications These encodings and size bounds are explicit practice assumptions. - `0 <= n <= 200000`. - The input represents one valid binary tree: all nodes are reachable from the root, there are no cycles, and each nonroot node has exactly one parent. - Each child identifier is `-1` or a valid node identifier. - Return `0` for an empty tree and `1` for a tree containing only its root. - A tree may be highly unbalanced. - Aim for `O(n)` time. ### Examples ```text children = [[1, 2], [-1, -1], [3, -1], [-1, -1]] Output: 3 ``` The longest root-to-leaf path visits nodes `0`, `2`, and `3`. ```text children = [] Output: 0 ``` ```hint Track depth along a traversal Each child is one level deeper than its parent. Consider how your traversal behaves when every node has only one child. ```