72. Edit Distance

哎，這么簡單的題目都沒做出來，有點想錯了，一開始想成1維dp，然后就很不好做了。不過1維也是可以用滾動數(shù)組做的，很難理解就是了。有點做不動了，上午就到這吧。

class Solution(object):
    def minDistance1(self, word1, word2):
        """
        :type word1: str
        :type word2: str
        :rtype: int
        """
        # O(m*n) space
        l1, l2 = len(word1)+1, len(word2)+1
        dp = [[0 for _ in xrange(l2)] for _ in xrange(l1)]
        for i in xrange(l1):
            dp[i][0] = i
        for j in xrange(l2):
            dp[0][j] = j
        for i in xrange(1, l1):
            for j in xrange(1, l2):
                dp[i][j] = min(dp[i-1][j]+1, dp[i][j-1]+1, dp[i-1][j-1]+(word1[i-1]!=word2[j-1]))
        return dp[-1][-1]
    
    # O(n) space with rolling array            
    def minDistance(self, word1, word2):
        l1, l2 = len(word1)+1, len(word2)+1
        dp = [0 for _ in xrange(l2)]
        for j in xrange(l2):
            dp[j] = j
            
        for i in xrange(1, l1):
            prev = i # when word1 is i length it will need i step to match word2 which is "" for now
            for j in xrange(1, l2):
                if word1[i-1] == word2[j-1]:
                    cur = dp[j-1]
                else:
                    cur = min(dp[j-1], prev, dp[j]) + 1
                dp[j-1] = prev
                prev = cur
            dp[l2-1] = prev
        return dp[-1]