<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>

DIRECTIONS = [(1, 0), (0, 1), (-1, 0), (0, -1)]

class Solution:
    def findWords(self, board: List[List[str]], words: List[str]) -> List[str]:
        prefixes = self.get_prefixes(words)
        if not board or not board[0]:
            return []
        res = set()
        words = set(words)
        visited = set()
        for i in range(len(board)):
            for j in range(len(board[0])):
                if board[i][j] in prefixes:
                    visited.add((i, j))
                    self.dfs(board, prefixes, i, j, board[i][j], visited, res)
                    visited.remove((i, j))
        return list(res)
        
    def dfs(self, board, prefixes, x, y, path, visited, res):
        if path in prefixes and prefixes[path]:
            res.add(path)
        if path not in prefixes:
            return
        
        for dx, dy in DIRECTIONS:
            newx, newy = x + dx, y + dy
            if not 0 <= newx < len(board):
                continue
            if not 0 <= newy < len(board[0]):
                continue
            if (newx, newy) in visited:
                continue

            visited.add((newx, newy))
            self.dfs(
                board, 
                prefixes, 
                newx, 
                newy, 
                path + board[newx][newy],
                visited,
                res
            )
            visited.remove((newx, newy))

    def get_prefixes(self, words):
        prefixes = {}
        for word in words:
            prefix = ''
            for char in word:
                prefix += char
                if prefix not in prefixes:
                    prefixes[prefix] = False
            prefixes[prefix] = True
        return prefixes
17300