Register Data Centers and Route to the Nearest Healthy Region

Problem Statement

You are tasked with building a routing engine for a globally distributed cloud platform. The engine maintains data center registrations and their operational health states, and routes incoming traffic to the nearest healthy data center using great-circle distance (the Haversine formula).

You must implement a function process_commands(commands: list[str]) -> list[str] that processes commands sequentially. Each command produces exactly one line of output. If a command fails validation, the state must not be modified, and it must output ERROR.

Commands

1. REGISTER

   • Registers a new data center with identifier `` at coordinates (, ).
   • Newly registered data centers default to health status UP.
   • Validation: must be non-empty, contain only alphanumeric characters, and not already be registered. must be a valid float in [-90.0, 90.0]. `` must be a valid float in [-180.0, 180.0].
   • Output: OK on success, ERROR on failure.

2. SET_STATUS

   • Updates the health status of data center ``.
   • `` must be either UP or DOWN.
   • Validation: must exist and must be valid.
   • Output: OK on success, ERROR on failure.

3. ROUTE

   • Finds the nearest data center with status UP from the query coordinates (, ) using Haversine distance.
   • Validation: must be in `[-90.0, 90.0]`, must be in [-180.0, 180.0], and there must be at least one data center with status UP.
   • Output: of the closest healthy data center. In case of a distance tie, pick the one with the lexicographically smallest. If validation fails, output ERROR.

Distance Formula

Given two coordinates (lat1, lon1) and (lat2, lon2) in degrees, convert angles to radians:

dlat = (lat2 - lat1) * pi / 180
dlon = (lon2 - lon1) * pi / 180
a = sin^2(dlat / 2) + cos(lat1 * pi / 180) * cos(lat2 * pi / 180) * sin^2(dlon / 2)
distance = 2 * R * asin(sqrt(a))

Use Earth's radius R = 6371.0 km.

Example

commands = [
    "REGISTER us-east 39.0438 -77.4874",
    "REGISTER eu-west 53.3498 -6.2603",
    "REGISTER us-east 40.0 -74.0",      # Duplicate ID
    "ROUTE 40.7128 -74.0060",          # NYC -> us-east is closer
    "SET_STATUS us-east DOWN",
    "ROUTE 40.7128 -74.0060",          # us-east is DOWN -> routes to eu-west
    "SET_STATUS eu-west DOWN",
    "ROUTE 40.7128 -74.0060"           # No UP data centers -> ERROR
]

# Output:
# ["OK", "OK", "ERROR", "us-east", "OK", "eu-west", "OK", "ERROR"]

Constraints

• Total number of commands: 1 <= len(commands) <= 5000.
• Number of unique data centers: <= 1000.
• Any malformed command or unknown command name must output ERROR without throwing an unhandled exception.