Word Break II

Given a string s and a dictionary of words dict, add spaces ins 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"].

	// DFS + Memorization
	public ArrayList<String> wordBreak(String s, Set<String> dict) {
		// Note: The Solution object is instantiated only once and is reused by
		// each test case.
		// min and max length of words in dictionary, used for
		// pruning.
		int min = Integer.MAX_VALUE;
		int max = Integer.MIN_VALUE;
		for (String str : dict) {
			min = Math.min(min, str.length());
			max = Math.max(max, str.length());
		}
		Map<String, ArrayList<String>> memorized = new HashMap<String, ArrayList<String>>();
		return wordBreakHelper(s, dict, min, max, memorized);
	}

	private ArrayList<String> wordBreakHelper(String s, Set<String> dict,
			int min, int max, Map<String, ArrayList<String>> memorized) {
		if (memorized.containsKey(s))
			return memorized.get(s);
		ArrayList<String> res = new ArrayList<String>();
		if (s == null || s.length() == 0)
			return res;
		if (dict.contains(s))
			res.add(s);
		// i pruning
		for (int i = min; i <= Math.min(s.length(), max); i++) {
			String prefix = s.substring(0, i);
			if (dict.contains(prefix)) {
				String suffix = s.substring(i);
				List<String> suffixBreak = wordBreakHelper(suffix, dict, min,
						max, memorized);
				if (!suffixBreak.isEmpty()) {
					for (String str : suffixBreak) {
						res.add(prefix + " " + str);
					}
				}
			}
		}
		memorized.put(s, res);
		return res;
	}

	// DP + back track
	public ArrayList<String> wordBreak2(String s, Set<String> dict) {
		int n = s.length();
		ArrayList<ArrayList<Integer>> pres = new ArrayList<ArrayList<Integer>>(
				n);
		// initialize
		for (int i = 0; i < n; ++i)
			pres.add(new ArrayList<Integer>());
		// DP. pres[i] stores position j where should insert space
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j <= i; ++j) {
				String suffix = s.substring(j, i + 1);
				if ((j == 0 || pres.get(j - 1).size() > 0) && dict.contains(suffix))
					pres.get(i).add(j);
			}
		}
		return getPath(s, n, pres);
	}

	public ArrayList<String> getPath(String s, int n, ArrayList<ArrayList<Integer>> pres) {
		ArrayList<String> res = new ArrayList<String>();
		for (int pre : pres.get(n - 1)) {
			if (pre == 0) {
				res.add(s.substring(0, n));
			} else {
				ArrayList<String> preres = getPath(s, pre, pres);
				String sub = s.substring(pre, n);
				for (String ss : preres)
					res.add(ss + " " + sub);
			}
		}
		return res;
	}