<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 Solution {
public:
    using SeenMap = unordered_map<int, unordered_set<int>>;
    struct TrieNode {
        TrieNode* next[26] = {nullptr};
        bool isEnd = false;
        int validChild = 0;
        TrieNode() {
            for (int i = 0; i < 26; i++) next[i] = nullptr;
        }

        void updateFromChild() {
            int newCnt = 0;
            for (int i = 0; i < 26; i++) {
                if (next[i]) {
                    newCnt += next[i]->validChild;
                }
            }
            validChild = newCnt;
        }

        void markSeen() {
            isEnd = false;
            --validChild;
        }
    };


    void add(TrieNode* root, const auto& string) {
        TrieNode* curr = root;
        for (char c: string) {
            if (!curr->next[c - 'a']) {
                curr->next[c-'a'] = new TrieNode();
            }
            curr->validChild++;
            curr = curr->next[c - 'a'];
        }
        curr->validChild++;
        curr->isEnd = true;
    }

    void add(TrieNode* root, const vector<string>& words) {
        for (const auto& w : words) add(root, w);
    }

    void dfs(vector<vector<char>>& board, SeenMap& seen, int r, int c, TrieNode* parent, string& buff, unordered_set<string>& res) {
        if (r < 0 || c < 0 || r >= board.size() || c >= board[0].size() || seen[r].contains(c)) return;
        char x = board[r][c];
        if (!parent->next[x-'a']) return;
        seen[r].insert(c);
        buff.push_back(x);
        
        auto curr = parent->next[x-'a'];
        if (curr->isEnd) {
            res.insert(buff);
            curr->markSeen();
        }
        

        if (curr->validChild > 0) {
            dfs(board, seen, r+1, c, curr, buff, res);
            dfs(board, seen, r-1, c, curr, buff, res);
            dfs(board, seen, r, c+1, curr, buff, res);
            dfs(board, seen, r, c-1, curr, buff, res);
        }
        curr->updateFromChild();
        buff.pop_back();
        seen[r].erase(c);
    }

    vector<string> findWords(vector<vector<char>>& board, vector<string>& words) {
        TrieNode* root = new TrieNode();
        add(root, words);
        
        unordered_set<string> result;
        for (int r = 0; r < board.size(); r++) {
            for (int c = 0; c < board[0].size(); c++) {
                SeenMap s;
                string buff = "";
                dfs(board, s, r, c, root, buff, result);
            }
        }
        return vector<string>(result.begin(), result.end());
    }
};
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