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/**

* Given a set of words (without duplicates), find all word squares you can

* build from them.

*

* A sequence of words forms a valid word square if the kth row and column read

* the exact same string, where 0 ≤ k < max(numRows, numColumns).

*

* For example, the word sequence ["ball","area","lead","lady"] forms a word

* square because each word reads the same both horizontally and vertically.

*

* b a l l

* a r e a

* l e a d

* l a d y

*

* Note:

* - There are at least 1 and at most 1000 words.

* - All words will have the exact same length.

* - Word length is at least 1 and at most 5.

* - Each word contains only lowercase English alphabet a-z.

*

* Example 1:

*

* Input:

* ["area","lead","wall","lady","ball"]

*

* Output:

* [

* [ "wall",

* "area",

* "lead",

* "lady"

* ],

* [ "ball",

* "area",

* "lead",

* "lady"

* ]

* ]

*

* Explanation:

* The output consists of two word squares. The order of output does not matter

* (just the order of words in each word square matters).

*

* Example 2:

*

* Input:

* ["abat","baba","atan","atal"]

*

* Output:

* [

* [ "baba",

* "abat",

* "baba",

* "atan"

* ],

* [ "baba",

* "abat",

* "baba",

* "atal"

* ]

* ]

*

* Explanation:

* The output consists of two word squares. The order of output does not matter

* (just the order of words in each word square matters).

*/

import java.util.List;

import java.util.ArrayList;

import java.util.Arrays;

public class WordSquares425 {

public List<List<String>> wordSquares(String[] words) {

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

if (words == null || words.length == 0 || words[0].length() == 0) return res;

int len = words[0].length();

TrieNode root = new TrieNode();

for (String word: words) root.addWord(word);

helper(new char[len][len], root, 0, len, new ArrayList<String>(), res);

return res;

}

private void helper(char[][] square, TrieNode root, int pos, int len, List<String> sqr, List<List<String>> res) {

if (pos == len) {

if (sqr.size() == len) {

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

for (String s: sqr) {

newSqr.add(s);

}

res.add(newSqr);

}

return;

}

List<String> finds = root.search(Arrays.copyOfRange(square[pos], 0, pos), len);

if (finds.size() == 0) return;

for (String w: finds) {

sqr.add(w);

for (int j=pos; j<len; j++) square[j][pos] = w.charAt(j);

helper(square, root, pos+1, len, sqr, res);

sqr.remove(sqr.size() - 1);

}

}

class TrieNode {

boolean isWord = false;

String word = null;

TrieNode[] children = new TrieNode[26];

public void addWord(String word) {

addWord(word.toCharArray(), 0);

}

public void addWord(char[] chars, int i) {

if (i == chars.length) {

this.isWord = true;

this.word = new String(chars);

return;

}

int idx = chars[i] - 'a';

if (children[idx] == null) {

TrieNode t = new TrieNode();

children[idx] = t;

}

children[idx].addWord(chars, i+1);

}

public List<String> search(char[] prefix, int length) {

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

search(prefix, length, 0, res);

return res;

}

public void search(char[] prefix, int length, int i, List<String> res) {

if (i == length) {

if (word != null) res.add(word);

return;

}

if (i < prefix.length) {

if (children[prefix[i] - 'a'] == null) return;

children[prefix[i] - 'a'].search(prefix, length, i+1, res);

} else {

for (TrieNode child: children) {

if (child != null) child.search(prefix, length, i+1, res);

}

}

}

}

public List<List<String>> wordSquares2(String[] words) {

Arrays.sort(words);

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

int W = words[0].length();

char[][] board = new char[W][W];

helper(board, 0, words, res, W);

return res;

}

private void helper(char[][] board, int i, String[] words, List<List<String>> res, int W) {

if (i >= W) {

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

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

r.add(new String(board[j]));

}

res.add(r);

return;

}

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

board[i][j] = 'a';

}

String start = new String(board[i]);

String prefix = new String(board[i], 0, i);

int idx = Arrays.binarySearch(words, start);

if (idx < 0) idx = - (idx + 1);

for (int k=idx; k<words.length; k++) {

String key = words[k];

if (!key.startsWith(prefix)) break;

char[] chars = key.toCharArray();

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

board[i][j] = chars[j];

}

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

board[j][i] = chars[j];

}

helper(board, i+1, words, res, W);

}

}

}