# Time:  O(n * l^2 + n * r), l is the max length of the words, 
#                            r is the number of the results.
# Space: O(n)
#
# Given a string s and a dictionary of words dict, 
# add spaces in s to construct a sentence where each word is a valid dictionary word.
# 
# Return all such possible sentences.
# 
# For example, given
# s = "catsanddog",
# dict = ["cat", "cats", "and", "sand", "dog"].
# 
# A solution is ["cats and dog", "cat sand dog"].
#

class Solution(object):
    def wordBreak(self, s, wordDict):
        """
        :type s: str
        :type wordDict: Set[str]
        :rtype: List[str]
        """
        n = len(s)

        max_len = 0
        for string in wordDict:
            max_len = max(max_len, len(string))

        can_break = [False for _ in xrange(n + 1)]
        valid = [[False] * n for _ in xrange(n)]
        can_break[0] = True
        for i in xrange(1, n + 1):
            for l in xrange(1, min(i, max_len) + 1):
                if can_break[i-l] and s[i-l:i] in wordDict:
                    valid[i-l][i-1] = True
                    can_break[i] = True

        result = []
        if can_break[-1]:
            self.genPath(s, valid, 0, [], result)
        return result
    
    def genPath(self, s, valid, start, path, result):
        if start == len(s):
            result.append(" ".join(path))
            return
        for i in xrange(start, len(s)):
            if valid[start][i]:
                path += [s[start:i+1]]
                self.genPath(s, valid, i + 1, path, result)
                path.pop()


if __name__ == "__main__":
    print Solution().wordBreak("catsanddog", ["cat", "cats", "and", "sand", "dog"])

# Time:  O(n * l^2 + n * r), l is the max length of the words, 
#                            r is the number of the results.
# Space: O(n)
#
# Given a string s and a dictionary of words dict, 
# add spaces in s to construct a sentence where each word is a valid dictionary word.
# 
# Return all such possible sentences.
# 
# For example, given
# s = "catsanddog",
# dict = ["cat", "cats", "and", "sand", "dog"].
# 
# A solution is ["cats and dog", "cat sand dog"].
#

class Solution(object):
    def wordBreak(self, s, wordDict):
        """
        :type s: str
        :type wordDict: Set[str]
        :rtype: List[str]
        """
        n = len(s)

        max_len = 0
        for string in wordDict:
            max_len = max(max_len, len(string))

        can_break = [False for _ in xrange(n + 1)]
        valid = [[False] * n for _ in xrange(n)]
        can_break[0] = True
        for i in xrange(1, n + 1):
            for l in xrange(1, min(i, max_len) + 1):
                if can_break[i-l] and s[i-l:i] in wordDict:
                    valid[i-l][i-1] = True
                    can_break[i] = True

        result = []
        if can_break[-1]:
            self.wordBreakHelper(s, valid, 0, [], result)
        return result
    
    def wordBreakHelper(self, s, valid, start, path, result):
        if start == len(s):
            result.append(" ".join(path))
            return
        for i in xrange(start, len(s)):
            if valid[start][i]:
                path += [s[start:i+1]]
                self.wordBreakHelper(s, valid, i + 1, path, result)
                path.pop()


if __name__ == "__main__":
    print Solution().wordBreak("catsanddog", ["cat", "cats", "and", "sand", "dog"])

Update word-break-ii.py