752 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 ofdeadendsdead 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 atargetrepresenting 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'.

The Idea: Run BFS. Begin with root '0000' and create 4 new edges, each of either rotate the number forwards and backwards. We can think of the deadends as areas already visited nodes in the graph. Ensure that no node is put in the graph twice, as this would perform the same computation twice. An example of a redundant computation may be: '0000' -> '0001' ->'0000'

Complexity: ??

import queue


class Solution:

    def rotate(self, pattern, pos, one):
        new = str((int(pattern[pos]) + one) % 10)
        return pattern[:pos] + new + pattern[pos + 1:]

    def openLock(self, deadends, target):
        """
        :type deadends: List[str]
        :type target: str
        :rtype: int
        """

        visited = set(deadends)
        if '0000' in visited:
            return -1
        visited.add('0000')
        q = queue.Queue()
        q.put(('0000', 0))
        while not q.empty():
            front, lvl = q.get()

            if front == target:
                return lvl

            for op in [-1,1]:
                for i in range(0, 4):
                    next_pat = self.rotate(front, i, op)
                    if next_pat not in visited:
                        # putting the if statement here ensured not TLE on OJ
                        if next_pat == target:
                            return lvl + 1
                        visited.add(next_pat)
                        q.put((next_pat, lvl + 1))
        return -1