<p>Given an <code>m x n</code> <code>board</code>&nbsp;of characters and a list of strings <code>words</code>, return <em>all words on the board</em>.</p>

<p>Each word must be constructed from letters of sequentially adjacent cells, where <strong>adjacent cells</strong> are horizontally or vertically neighboring. The same letter cell may not be used more than once in a word.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/07/search1.jpg" style="width: 322px; height: 322px;" />
<pre>
<strong>Input:</strong> board = [[&quot;o&quot;,&quot;a&quot;,&quot;a&quot;,&quot;n&quot;],[&quot;e&quot;,&quot;t&quot;,&quot;a&quot;,&quot;e&quot;],[&quot;i&quot;,&quot;h&quot;,&quot;k&quot;,&quot;r&quot;],[&quot;i&quot;,&quot;f&quot;,&quot;l&quot;,&quot;v&quot;]], words = [&quot;oath&quot;,&quot;pea&quot;,&quot;eat&quot;,&quot;rain&quot;]
<strong>Output:</strong> [&quot;eat&quot;,&quot;oath&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/07/search2.jpg" style="width: 162px; height: 162px;" />
<pre>
<strong>Input:</strong> board = [[&quot;a&quot;,&quot;b&quot;],[&quot;c&quot;,&quot;d&quot;]], words = [&quot;abcb&quot;]
<strong>Output:</strong> []
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == board.length</code></li>
	<li><code>n == board[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 12</code></li>
	<li><code>board[i][j]</code> is a lowercase English letter.</li>
	<li><code>1 &lt;= words.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words[i].length &lt;= 10</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>words</code> are unique.</li>
</ul>

class Trie:
    def __init__(self, words=[]):
        self.root = {"length": 0}
        for word in words:
            self.insert(word)
            
    def insert(self, word):
        current = self.root
        for c in word:
            if c not in current:
                current[c] = {"length": 0}
            current["length"] += 1
            current = current[c]
        current["length"] += 1
        current["?"] = True

    def remove(self, word):
        current = self.root
        current["length"] -= 1
        for i, c in enumerate(word):
            if c in current:
                current[c]["length"] -= 1
                if current[c]["length"] < 1:
                    current.pop(c)
                    break
                else:
                    current = current[c]
        if i == len(word) - 1 and "?" in current:
            current.pop("?")

    def contains(self, word):
        current = self.root
        for c in word:
            if c not in current:
                return 0
            current = current[c]
        return 2 if "?" in current else 1
@cache
class Solution:
    def findWords(self, board: List[List[str]], words: List[str]) -> List[str]:
        NUM_ROWS, NUM_COLS = len(board), len(board[0])
        seq_two = set()
        candidates = []
        reversed_words = set()
        
        for i in range(NUM_ROWS):
            for j in range(NUM_COLS - 1):
                seq_two.add(board[i][j] + board[i][j + 1])
        for j in range(NUM_COLS):
            for i in range(NUM_ROWS - 1):
                seq_two.add(board[i][j] + board[i + 1][j])
                
        for word in words:
            in_board = True
            for i in range(len(word) - 1):
                if (
                    word[i : i + 2] not in seq_two
                    and word[i + 1] + word[i] not in seq_two
                ):
                    in_board = False
                    break
            if not in_board:
                continue
            if word[:4] == word[0] * 4:
                word = word[::-1]
                reversed_words.add(word)
            candidates.append(word)
            
        res = set()
        trie = Trie(candidates)

        def dfs(row, col, current):
            current.append(board[row][col])
            board[row][col] = "."
            found = trie.contains(current)
            if not found:
                board[row][col] = current.pop()
                return
            if found == 2:
                w = "".join(current)
                if w in reversed_words:
                    res.add(w[::-1])
                    reversed_words.remove(w)
                else:
                    res.add(w)
                trie.remove(w)
            dirs = ((0, 1), (0, -1), (1, 0), (-1, 0))
            for di, dj in dirs:
                i, j = row + di, col + dj
                if (
                    0 <= i < NUM_ROWS
                    and 0 <= j < NUM_COLS
                    and board[i][j] != "."
                ):
                    dfs(i, j, current)
            board[row][col] = current.pop()

        for i in range(NUM_ROWS):
            for j in range(NUM_COLS):
                dfs(i, j, [])
        return list(res)
17100