<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 Node {
public:
    int count;
    char ch;
    Node*prv=nullptr;
    unordered_map<char,Node*>child;

    Node(): count(0), ch('#'){}
    Node(char ch): count(0), ch(ch){}
    Node(char ch, Node*prv): count(0), ch(ch),prv(prv){}
};



class Trie {
public:
    Node* root;

    Trie() { 
        root = new Node();
    }

    ~Trie() {
        delete_node(root);
    }
    
    void insert(string word) {
        Node* p=root;
        for(char ch:word){
            if(p->child.find(ch)==p->child.end()){
                p->child[ch]=new Node(ch,p);
            }
            p=p->child[ch];
        }
        p->count++;
    }
    
    bool search(string word) {
        Node* p=root;
        for(char ch:word){
            if(p->child.find(ch)==p->child.end())return false;
            p=p->child[ch];
        }
        return p->count>0;
    }
    
    bool startsWith(string prefix) {
        Node* p=root;
        for(char ch:prefix){
            if(p->child.find(ch)==p->child.end())return false;
            p=p->child[ch];
        }
        return true;
    }

private:
    void delete_node(Node* node) {
        if(node==nullptr)return;
        for(auto&ch:node->child)delete_node(ch.second);
        delete node;
    }
};

vector<pair<int,int>>dir={{-1,0},{1,0},{0,-1},{0,1}};

void verify(vector<vector<char>>&board,int h,int w,char ch,Node*node,vector<string>&sol,string&pth,unordered_set<int>&vis){
    int H=board.size(),W=board[0].size();
    pth+=board[h][w];
    vis.insert(h*W+w);
    if(node->count){
        sol.push_back(pth),node->count--;
        if(!node->count){
            Node*p=node;
            while(p!=nullptr&&!p->count&&p->child.empty()){
                char tmp=p->ch;
                p=p->prv;
                if(p!=nullptr)p->child.erase(tmp);
            }
        }
    }
    if(node->child.empty()){
        vis.erase(h*W+w);
        pth.erase(pth.size()-1);
        return;
    }
    for(const auto&d:dir){
        int nh=h+d.first,nw=w+d.second;
        if(nh>=0&&nh<H&&nw>=0&&nw<W&&vis.find(nh*W+nw)==vis.end()){
            if(node->child.find(board[nh][nw])!=node->child.end()){
                verify(board,nh,nw,board[nh][nw],node->child[board[nh][nw]],sol,pth,vis);
            }
        }
    }
    vis.erase(h*W+w);
    pth.erase(pth.size()-1);
}


void traverse(vector<vector<char>>&board,Trie*trie,vector<string>&sol){
    Node* root=trie->root;
    int H=board.size(),W=board[0].size();
    for(int h=0;h<H;h++)for(int w=0;w<W;w++){
        char ch=board[h][w];
        if(root->child.find(ch)!=root->child.end()){
            unordered_set<int>vis;
            string pth="";
            verify(board,h,w,ch,root->child[ch],sol,pth,vis);
        }
    }
}


class Solution {
public:
    vector<string> findWords(vector<vector<char>>& board, vector<string>& words) {
        Trie*trie=new Trie();
        for(string&word:words)trie->insert(word);
        vector<string>sol;
        traverse(board,trie,sol);
        return sol;
    }
};
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