Problem

A cybersecurity team at a healthcare SaaS provider scans customer “export bundles” before they’re uploaded to cloud storage. Each bundle is represented as a nested JSON-like object (Python dict) describing a directory tree. With millions of daily exports, the scanner needs a fast way to flatten this structure into a list of full file paths so downstream services can apply allow/deny rules and compute checksums.

You are given a nested object where:

• Directories are represented by dictionaries (dict[str, Any]).
• Files are represented by non-dictionary values (e.g., None, integers, strings). The value is metadata you should preserve.

Implement flatten_directory(tree) that returns a flat dictionary mapping each full path to the corresponding file metadata.

Path rules

1. Use / as the separator.
2. The root has no leading / (e.g., root/a.txt, not /root/a.txt).
3. Only files appear in the output; empty directories contribute nothing.
4. Keys in the input do not contain /.

Formal signature

• Input: tree: dict[str, Any]
• Output: dict[str, Any] where each key is a full path and each value is the original metadata.

Examples

Example 1

Input

{
  "root": {
    "docs": {"readme.md": 1200},
    "bin": {"app": {"main.py": "sha256:abc"}},
    "empty": {},
    "license.txt": null
  }
}

Output

{
  "root/docs/readme.md": 1200,
  "root/bin/app/main.py": "sha256:abc",
  "root/license.txt": null
}

Explanation: Only leaf nodes that are files are emitted; empty is ignored.

Example 2

Input

{"a": {"b": {"c.txt": 1}}, "x.log": 0}

Output

{"a/b/c.txt": 1, "x.log": 0}

Explanation: The function collects paths from multiple roots.

Constraints

• 1 <= number_of_nodes <= 2 * 10^5
• Maximum nesting depth <= 10^4
• Directory keys are non-empty strings without /
• File metadata can be any JSON-serializable value (treat as opaque)

Notes

• Your solution should be efficient for large trees.
• Avoid recursion depth issues in Python for deeply nested inputs.