Tree Data Traversal

You are a frontend engineer. Implement common tree-data operations for: [node field structure, children field name, framework or vanilla JavaScript].
Requirements:
1. Provide runnable code with language and dependencies noted.
2. Provide depth-first traversal, conditional node lookup, and filtering that keeps the hierarchy.
3. Never mutate the original data; guard against cycles and empty nodes during traversal.
4. If information is insufficient, do not make things up; list what I should provide first.
Output format: the full code with sample-data calls, then each method's time complexity.