Tree Backend: Design a REST API for Managing a Hierarchical Tree Structure

Question

## Problem

Design a backend API for managing hierarchical data (e.g., org charts, category trees). Each node has an `id`, `name`, `parent_id`, and optional `metadata`. Implement these endpoints:

```
POST   /nodes              - create a node (specify parent_id or null for root)
GET    /nodes/:id          - get a node and its direct children
GET    /nodes/:id/subtree  - get a node and all descendants
PUT    /nodes/:id          - update name or metadata
DELETE /nodes/:id          - delete node and all descendants
PUT    /nodes/:id/move     - move subtree to a new parent
```

## Example

```
POST /nodes  {"name": "Engineering", "parent_id": null}         -> {"id": "1"}
POST /nodes  {"name": "Backend",     "parent_id": "1"}          -> {"id": "2"}
POST /nodes  {"name": "Frontend",    "parent_id": "1"}          -> {"id": "3"}
GET  /nodes/1/subtree  -> {"id":"1", "children": [{"id":"2"}, {"id":"3"}]}
PUT  /nodes/2/move  {"new_parent_id": "3"}  -> Backend becomes child of Frontend
```

## Follow-ups

1. What database representation (adjacency list, nested sets, closure table, path enumeration) fits best for this use case?
2. How do you implement `GET /subtree` efficiently without loading the whole table?
3. How do you prevent a `move` operation from creating a cycle?

Tree Backend: Design a REST API for Managing a Hierarchical Tree Structure

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