The 2^N Migration Black Hole
#devops-critical — CI pipeline hung 14 hours on shard migration
DevOps: Migration uses 3-peg Tower of Hanoi logic. Works for 10 shards. At 60 shards it needs (2^60) - 1 moves — ~36 billion years at one move per second.
The trap: O(2^N) cannot be optimized away. The fix is fail fast, not faster code.
Your task
Fix `preflight_complexity_check()` in `shard_migrator.py`: calculate (2^N) - 1, abort if it exceeds MAX_PRODUCTION_OPS, explain exponential complexity.
Book: write the recursion · Prod: algorithmic circuit breaker before CI hangs forever.
Skills you'll prove
Interview Tip
When asked about algorithmic complexity or system design, say: "Some algorithms are mathematically doomed — you cannot code your way out of O(2^N). I once saw a migration script use Tower of Hanoi logic with one staging cluster. At 10 shards it finished in a second. At 60 shards it needed over a quintillion moves. The fix was not faster Python — it was a preflight complexity check that calculated (2^N) - 1, aborted before execution, and forced architects to add a fourth buffer cluster. In production, a script that hangs for billions of years is worse than one that fails in a millisecond with a clear error."