# Time:  O(k * n^k + d), n is the number of alphabets,
#                        k is the length of target,
#                        d is the size of deadends
# Space: O(k * n^k + d)

# 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'.

class Solution(object):
    def openLock(self, deadends, target):
        """
        :type deadends: List[str]
        :type target: str
        :rtype: int
        """
        dead = set(deadends)
        q = ["0000"]
        lookup = {"0000"}
        depth = 0
        while q:
            next_q = []
            for node in q:
                if node == target: return depth
                if node in dead: continue
                for i in xrange(4):
                    n = int(node[i])
                    for d in (-1, 1):
                        nn = (n+d) % 10
                        neighbor = node[:i] + str(nn) + node[i+1:]
                        if neighbor not in lookup:
                            lookup.add(neighbor)
                            next_q.append(neighbor)
            q, next_q = next_q, []
            depth += 1
        return -1

Create open-the-lock.py