Given a non-empty string s and a dictionary wordDict containing a list of non-empty words, add spaces in s to construct a sentence where each word is a valid dictionary word. You may assume the dictionary does not contain duplicate words.
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"].

Solution：Backtracking + dp

思路：
Time Complexity: O(num_word * s.length) Space Complexity: O()

Solution Code：

class Solution {
    public List<String> wordBreak(String s, List<String> wordList) {
        Set<String> wordDict = new HashSet<>();
        for(String word: wordList) wordDict.add(word);
        
        return DFS(s, wordDict, new HashMap<String, LinkedList<String>>());
    }       

    // DFS function returns an array including all substrings derived from s.
    List<String> DFS(String s, Set<String> wordDict, HashMap<String, LinkedList<String>> map) {
        if (map.containsKey(s)) 
            return map.get(s);

        LinkedList<String>res = new LinkedList<String>();     
        if (s.length() == 0) {
            res.add("");
            return res;
        }               
        for (String word : wordDict) {
            if (s.startsWith(word)) {
                List<String>sublist = DFS(s.substring(word.length()), wordDict, map);
                for (String sub : sublist) 
                    res.add(word + (sub.isEmpty() ? "" : " ") + sub);               
            }
        }       
        map.put(s, res);
        return res;
    }
}