// Memory Limit Exceeded

// public List<String> wordBreak(String s, List<String> wordDict) {

// int N = s.length();

// LinkedList<String>[] dp = new LinkedList[N+1];

// for (int i=0; i<=N; i++) dp[i] = new LinkedList<>();

// Set<String> wordSet = new HashSet<>(wordDict);

// dp[0].add("");

// for (int i=1; i<=N; i++) {

// for (int j=0; j<i; j++) {

// String w = s.substring(j, i);

// if (dp[j].size() > 0 && wordSet.contains(w)) {

// for (String p: dp[j]) {

// dp[i].add(p.length() == 0 ? w : (p + " " + w));

// }

// }

// }

// }

// return dp[N];

// }

// DP

public List<String> wordBreak(String s, List<String> wordDict) {

Set<String> wordSet = new HashSet<>(wordDict);

if (!wordIsBreakable(s, wordSet)) return new ArrayList<>();

return wordBreak(s, wordSet);

}

public List<String> wordBreak(String s, Set<String> wordDict) {

LinkedList<String>[] dp = new LinkedList[s.length() + 1];

LinkedList<String> initial = new LinkedList<>();

initial.add("");

dp[0] = initial;

for (int i = 1; i <= s.length(); i++) {

LinkedList<String> list = new LinkedList<>();

for (int j = 0; j < i; j++) {

if (dp[j].size() > 0 && wordDict.contains(s.substring(j, i))) {

for (String l : dp[j]) {

list.add(l + (l.equals("") ? "" : " ") + s.substring(j, i));

}

}

}

dp[i] = list;

}

return dp[s.length()];

}

public boolean wordIsBreakable(String s, Set<String> wordDictSet) {

boolean[] dp = new boolean[s.length() + 1];

dp[0] = true;

for (int i = 1; i <= s.length(); i++) {

for (int j = 0; j < i; j++) {

if (dp[j] && wordDictSet.contains(s.substring(j, i))) {

dp[i] = true;

break;

}

}

}

return dp[s.length()];

}

// Backtracing

public List<String> wordBreak2(String s, List<String> wordDict) {

if (!wordIsBreakable(s, new HashSet<>(wordDict))) return new ArrayList<>();

int N = s.length();

Set<String>[] dp = new Set[N];

for (int i=0; i<N; i++) dp[i] = new HashSet<String>();

for (int i=0; i<N; i++) {

for (String word: wordDict) {

if (s.startsWith(word, i)) {

dp[i].add(word);

}

}

}

List<String> res = new ArrayList<>();

helper(N, dp, res, new StringBuilder(), 0);

return res;

}

private void helper(int N, Set<String>[] dp, List<String> res, StringBuilder sb, int i) {

if (i == N) {

res.add(sb.substring(0, sb.length()-1).toString());

return;

}

for (String w: dp[i]) {

sb.append(w).append(" ");

helper(N, dp, res, sb, i+w.length());

sb.delete(sb.length()-w.length()-1, sb.length());

}

}

/**

public List<String> wordBreak3(String s, Set<String> wordDict) {

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;

}