Stretch Problem: Open the Lock (medium)

This problem is optional. The problems above cover what the chapter teaches. This one is here for readers who want a harder queue question, and nothing later in the course depends on it.

Problem Statement

A lock has four wheels, and each wheel shows one digit from 0 to 9. A wheel can be turned one step in either direction, so 9 turns to 0 and 0 turns back to 9. Each single turn of a single wheel counts as one move.

The lock starts at "0000". Some settings are dead ends: if the lock ever shows one of them it stops working and cannot be turned again.

Given the array