752 Open the Lock.py

#!/usr/bin/python3
"""
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:
The length of deadends will be in the range [1, 500].
target will not be in the list deadends.
Every string in deadends and the string target will be a string of 4 digits from
the 10,000 possibilities '0000' to '9999'.
"""
from typing import List


class Solution:
    def openLock(self, deadends: List[str], target: str) -> int:
        """
        bfs
        """
        destination = tuple(int(c) for c in target)
        deadends_set = set(
            tuple(int(c) for c in s)
            for s in deadends
        )
        q = [(0, 0, 0, 0)]
        if q[0] in deadends_set:
            return -1

        step = 0
        visited = set(q)
        while q:
            cur_q = []
            for e in q:
                if e == destination:
                    return step
                for i in range(4):
                    for delta in (-1, 1):
                        nxt_lst = list(e)  # copy
                        nxt_lst[i] = (nxt_lst[i] + delta) % 10  # forward or backward
                        nxt = tuple(nxt_lst)
                        if nxt not in visited and nxt not in deadends_set:
                            visited.add(nxt)
                            cur_q.append(nxt)

            step += 1
            q = cur_q

        return -1


if __name__ == "__main__":
    assert Solution().openLock(["8888"], "0009") == 1
    assert Solution().openLock(["8887","8889","8878","8898","8788","8988","7888","9888"], "8888") == -1