<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:
    vector<vector<char>> board;
    map<char, vector<pair<int,int>>> mp;
    vector<pair<int,int>> path;
    vector<vector<pair<int,int>>> coords;

    bool test_rest(int index){
        for (int i=index; i<coords.size(); i++){
            for (pair<int,int>p:coords[i]){
                if (abs(p.first-path[i-1].first) + abs(p.second-path[i-1].second) == 1){
                    bool in = false;
                    for (int j=0; j<i; j++){
                        if (p==path[j]){
                            in = true;
                        }
                    }
                    if (!in){
                        path[i] = p;
                        if (test_rest(i+1)){
                            return true;
                        }
                    }
                }
            }
            return false;
        }
        return true;
    }

    bool inGrid(string& word){
        coords = {};
        for (char c:word){
            if (mp.find(c) == mp.end()){
                return false;
            } else{
                coords.push_back(mp[c]);
            }
        }
        if (coords.size() == 1){
            return true;
        }
        if (coords[coords.size()-1].size() < coords[0].size()){
            reverse(coords.begin(), coords.end());
        }
        path = {};
        for (vector<pair<int,int>> start:coords){
            path.push_back(start[0]);
        }
        bool valid = false;
        for (pair<int,int> start:coords[0]){
            path[0] = start;
            if (test_rest(1)){
                return true;
            }
        }
        return false;
    }

    vector<string> findWords(vector<vector<char>>& board, vector<string>& words) {
        vector<string> out = {};
        this->board = board;
        for (int i=0; i<board.size(); i++){
            for (int j=0; j<board[0].size(); j++){
                if (mp.find(board[i][j]) == mp.end()){
                    mp[board[i][j]] = {};
                }
                mp[board[i][j]].push_back(pair<int,int>(i,j));
            }
        }
        for (string word:words){
            if (inGrid(word)){
                out.push_back(word);
            }
        }
        return out;
    }
};
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