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Solution: Recover a Tree From Preorder Traversal

Explore how to rebuild a binary tree from a preorder traversal string that encodes node depths with dashes. Learn to apply a depth-first search algorithm that parses depths and values in a single pass, efficiently handling tree structure with recursion and understanding the approach's time and space complexity.

Statement

We perform a preorder depth-first traversal on a binary tree starting from its root.

  • For each node, we first write D dashes, where D is the depth of the node in the tree, followed by the node’s integer value.

  • The root node has depth 0.

  • If a node is at depth D, its children (if any) will appear at depth D + 1.

  • If a node has only one child, it will always be the left child.

You are given the string representation of this traversal. Your task is to reconstruct the original binary tree and return its root.

Constraints:

  • The number of nodes in the original binary tree lies within the range [1,500][1, 500].

  • 11 \leq node.data 103 ...