<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:
    int x[4] = {0, 1, 0, -1};
    int y[4] = {1, 0, -1, 0};
    struct TreeNode
    {
        char c;
        int index;
        unordered_map<char, TreeNode*> children;
        TreeNode(char val) {c = val;}
    };

    TreeNode *root;
    int m, n, k;
    vector<vector<bool>> visited;
    vector<string> findWords(vector<vector<char>>& board, vector<string>& words)
    {
        m = board.size();
        n = board[0].size();
        k = words.size();
        root = new TreeNode('0');
        visited.assign(m, vector<bool>(n, false));
        for(int i=0;i<k;i++)
        {
            TreeNode* node = root;
            for(char &cc:words[i])
            {
                if(node->children.find(cc)==node->children.end()) node->children[cc] = new TreeNode(cc);
                node = node->children[cc];
            }
            node->children[' '] = new TreeNode(' ');
            node->children[' ']->index = i;
        }

        unordered_set<int> indices;
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<n;j++)
            {
                unordered_set<int> stringpos = search(board, i, j, root);
                if(!stringpos.empty()) 
                {
                    for(auto it=stringpos.begin();it!=stringpos.end();it++)
                    {
                        indices.insert(*it);
                        remove(words[*it], root, 0);
                    }
                }
            }
            if(indices.size()==k) return words;
        }
        vector<string> ans;
        ans.reserve(indices.size());
        for(auto it=indices.begin();it!=indices.end();it++)
        {
            ans.push_back(words[*it]);
        }
        return ans;
    }

    void remove(string &s, TreeNode* parent, int i)
    {
        if(i==s.length())
        {
            delete parent->children[' '];
            parent->children.erase(' ');
            return;
        }
        remove(s, parent->children[s[i]], i+1);
        if(parent->children[s[i]]->children.empty()) 
        {
            delete parent->children[s[i]];
            parent->children.erase(s[i]);
        }
    }

    bool isValid(int &i, int &j)
    {
        if(i<0 || i>=m || j<0 || j>=n) return false;
        return !visited[i][j];
    }

    unordered_set<int> search(vector<vector<char>>& board, int i, int j, TreeNode* node)
    {
        if(node->children.find(board[i][j])==node->children.end()) return unordered_set<int>();
        visited[i][j] = true;
        TreeNode *nn = node->children[board[i][j]];
        unordered_set<int> ans;
        for(int dir=0;dir<4;dir++)
        {
            int newi = i+x[dir];
            int newj = j+y[dir];
            if(isValid(newi, newj))
            {
                unordered_set<int> gg = search(board, newi, newj, nn);
                ans.insert(gg.begin(), gg.end());
            }
        }
        if(nn->children.find(' ')!=nn->children.end()) ans.insert(nn->children[' ']->index);
        visited[i][j] = false;
        return ans;
    }
};
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