Minimum Unique Word Abbreviation — Python

# Time:  O((d + n) * 2^n)
# Space: O(d)

# optimized from Solution2
class Solution(object):
    def minAbbreviation(self, target, dictionary):
        """
        :type target: str
        :type dictionary: List[str]
        :rtype: str
        """
        def bits_to_abbr_len(targets, bits):
            total = 0
            pre = 0
            for i in xrange(len(target)):
                if bits & 1:
                    if i - pre > 0:
                        total += len(str(i - pre))
                    pre = i + 1
                    total += 1
                elif i == len(target) - 1:
                    total += len(str(i - pre + 1))
                bits >>= 1
            return total

        def bits_to_abbr(targets, bits):
            abbr = []
            pre = 0
            for i in xrange(len(target)):
                if bits & 1:
                    if i - pre > 0:
                        abbr.append(str(i - pre))
                    pre = i + 1
                    abbr.append(target[i])
                elif i == len(target) - 1:
                    abbr.append(str(i - pre + 1))
                bits >>= 1
            return "".join(abbr)
  
        diffs = []
        for word in dictionary:
            if len(word) != len(target):
                continue
            diffs.append(sum(2**i for i, c in enumerate(word) if target[i] != c))

        if not diffs:
            return str(len(target))

        result = 2**len(target)-1
        for mask in xrange(2**len(target)):
            if all(d & mask for d in diffs) and bits_to_abbr_len(target, mask) < bits_to_abbr_len(target, result):
                result = mask
        return bits_to_abbr(target, result)
    

# Time:  O((d + n) * 2^n)
# Space: O(d + n)
class Solution2(object):
    def minAbbreviation(self, target, dictionary):
        """
        :type target: str
        :type dictionary: List[str]
        :rtype: str
        """
        def bits_to_abbr(targets, bits):
            abbr = []
            pre = 0
            for i in xrange(len(target)):
                if bits & 1:
                    if i - pre > 0:
                        abbr.append(str(i - pre))
                    pre = i + 1
                    abbr.append(target[i])
                elif i == len(target) - 1:
                    abbr.append(str(i - pre + 1))
                bits >>= 1
            return "".join(abbr)
  
        diffs = []
        for word in dictionary:
            if len(word) != len(target):
                continue
            diffs.append(sum(2**i for i, c in enumerate(word) if target[i] != c))

        if not diffs:
            return str(len(target))

        result = target
        for mask in xrange(2**len(target)):
            abbr = bits_to_abbr(target, mask)
            if all(d & mask for d in diffs) and len(abbr) < len(result):
                result = abbr
        return result