752\. Open the Lock

Medium

You have a lock in front of you with 4 circular wheels. Each wheel has 10 slots: `'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'`. The wheels can rotate freely and wrap around: for example we can turn `'9'` to be `'0'`, or `'0'` to be `'9'`. Each move consists of turning one wheel one slot.

The lock initially starts at `'0000'`, a string representing the state of the 4 wheels.

You are given a list of `deadends` dead ends, meaning if the lock displays any of these codes, the wheels of the lock will stop turning and you will be unable to open it.

Given a `target` representing the value of the wheels that will unlock the lock, return the minimum total number of turns required to open the lock, or -1 if it is impossible.

**Example 1:**

**Input:** deadends = ["0201","0101","0102","1212","2002"], target = "0202"

**Output:** 6

**Explanation:** 

A sequence of valid moves would be "0000" -> "1000" -> "1100" -> "1200" -> "1201" -> "1202" -> "0202". 

Note that a sequence like "0000" -> "0001" -> "0002" -> "0102" -> "0202" would be invalid, 

because the wheels of the lock become stuck after the display becomes the dead end "0102".

**Example 2:**

**Input:** deadends = ["8888"], target = "0009"

**Output:** 1

**Explanation:** We can turn the last wheel in reverse to move from "0000" -> "0009".

**Example 3:**

**Input:** deadends = ["8887","8889","8878","8898","8788","8988","7888","9888"], target = "8888"

**Output:** -1

**Explanation:** We cannot reach the target without getting stuck.

**Constraints:**

*   `1 <= deadends.length <= 500`
*   `deadends[i].length == 4`
*   `target.length == 4`
*   target **will not be** in the list `deadends`.
*   `target` and `deadends[i]` consist of digits only.