# Open the Lock

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 can't reach the target without getting stuck.
```

**Example 4:**\\

```
Input: deadends = ["0000"], target = "8888"
Output: -1
```

**Note:**\\

1. The length of `deadends` will be in the range `[1, 500]`.
2. `target` will not be in the list `deadends`.
3. Every string in `deadends` and the string `target` will be a string of 4 digits from the 10,000 possibilities `'0000'` to `'9999'`.

```java
class Solution {
    public static int openLock(String[] deadends, String target) {
        Queue<String> q = new LinkedList<>();
        Set<String> visited = new HashSet<>(Arrays.asList(deadends));
        int depth = 0;
        q.add("0000");
        while (!q.isEmpty()) {
            int size = q.size();
            for (int i = 0; i < size; i++) {
                String node = q.poll();
                if (node.equals(target))
                    return depth;
                if (visited.contains(node))
                    continue;
                visited.add(node);
                q.addAll(getSuccessors(node));
            }
            depth++;
        }
        return -1;
    }

    private static List<String> getSuccessors(String str) {
        List<String> res = new LinkedList<>();
        for (int i = 0; i < str.length(); i++) {
            res.add(str.substring(0, i) + (str.charAt(i) == '0' ? 9 : str.charAt(i) - '0' - 1) + str.substring(i + 1));
            res.add(str.substring(0, i) + (str.charAt(i) == '9' ? 0 : str.charAt(i) - '0' + 1) + str.substring(i + 1));
        }
        return res;
    }
}
```
