Number of Ways to Form a Target String Given a Dictionary — Python

# Time:  O(l * (w + n)), l is the length of a word, w is the number of words, n is the length of target
# Space: O(n)

import collections


# optimized from Solution2
class Solution(object):
    def numWays(self, words, target):
        """
        :type words: List[str]
        :type target: str
        :rtype: int
        """
        MOD = 10**9+7
        dp = [0]*(len(target)+1)
        dp[0] = 1
        for i in xrange(len(words[0])):
            count = collections.Counter(w[i] for w in words)
            for j in reversed(xrange(len(target))):
                dp[j+1] += dp[j]*count[target[j]] % MOD
        return dp[-1] % MOD


# Time:  O(l * (w + n)), l is the length of a word, w is the number of words, n is the length of target
# Space: O(n)
import collections


class Solution2(object):
    def numWays(self, words, target):
        """
        :type words: List[str]
        :type target: str
        :rtype: int
        """
        MOD = 10**9+7
        # dp[i+1][j+1]: number of ways of target[0..j] using count[0..i].
        dp = [[0]*(len(target)+1) for _ in xrange(2)]
        for i in xrange(len(dp)):
            dp[i][0] = 1
        for i in xrange(len(words[0])):
            count = collections.Counter(w[i] for w in words)
            for j in reversed(xrange(len(target))):
                dp[(i+1)%2][j+1] = dp[i%2][j+1]+dp[i%2][j]*count[target[j]] % MOD
        return dp[(len(words[0]))%2][-1] % MOD