Freedom Trail — Python

# Time:  O(k) ~ O(k * r^2)
# Space: O(r)

import collections


class Solution(object):
    def findRotateSteps(self, ring, key):
        """
        :type ring: str
        :type key: str
        :rtype: int
        """
        lookup = collections.defaultdict(list)
        for i in xrange(len(ring)):
            lookup[ring[i]].append(i)

        dp = [[0] * len(ring) for _ in xrange(2)]
        prev = [0]
        for i in xrange(1, len(key)+1):
            dp[i%2] = [float("inf")] * len(ring)
            for j in lookup[key[i-1]]:
                for k in prev:
                    dp[i%2][j] = min(dp[i%2][j],
                                     min((k+len(ring)-j) % len(ring), \
                                         (j+len(ring)-k) % len(ring)) + \
                                     dp[(i-1) % 2][k])
            prev = lookup[key[i-1]]
        return min(dp[len(key)%2]) + len(key)