<p>Given an <code>m x n</code> grid of characters <code>board</code> and a string <code>word</code>, return <code>true</code> <em>if</em> <code>word</code> <em>exists in the grid</em>.</p>

<p>The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/04/word2.jpg" style="width: 322px; height: 242px;" />
<pre>
<strong>Input:</strong> board = [[&quot;A&quot;,&quot;B&quot;,&quot;C&quot;,&quot;E&quot;],[&quot;S&quot;,&quot;F&quot;,&quot;C&quot;,&quot;S&quot;],[&quot;A&quot;,&quot;D&quot;,&quot;E&quot;,&quot;E&quot;]], word = &quot;ABCCED&quot;
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/04/word-1.jpg" style="width: 322px; height: 242px;" />
<pre>
<strong>Input:</strong> board = [[&quot;A&quot;,&quot;B&quot;,&quot;C&quot;,&quot;E&quot;],[&quot;S&quot;,&quot;F&quot;,&quot;C&quot;,&quot;S&quot;],[&quot;A&quot;,&quot;D&quot;,&quot;E&quot;,&quot;E&quot;]], word = &quot;SEE&quot;
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/10/15/word3.jpg" style="width: 322px; height: 242px;" />
<pre>
<strong>Input:</strong> board = [[&quot;A&quot;,&quot;B&quot;,&quot;C&quot;,&quot;E&quot;],[&quot;S&quot;,&quot;F&quot;,&quot;C&quot;,&quot;S&quot;],[&quot;A&quot;,&quot;D&quot;,&quot;E&quot;,&quot;E&quot;]], word = &quot;ABCB&quot;
<strong>Output:</strong> false
</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;= 6</code></li>
	<li><code>1 &lt;= word.length &lt;= 15</code></li>
	<li><code>board</code> and <code>word</code> consists of only lowercase and uppercase English letters.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> Could you use search pruning to make your solution faster with a larger <code>board</code>?</p>

class Solution {
public:
    bool exist(vector<vector<char>>& board, string word) {
        if (word.size() > board.size() * board.front().size()) return false;

        for (auto c : word) {
            bool found_in_board = false;
            for (const auto& row : board) {
                for (const auto& cell : row) {
                    if (cell == c) {
                        found_in_board = true;
                        break;
                    }
                }
            }
            if (!found_in_board) {
                return false;
            }
        }

        for (size_t i = 0; i < board.size(); ++i) {
            for (size_t j = 0; j < board[i].size(); ++j) {
                if (board[i][j] == word.at(0)) {
                    set<pair<size_t, size_t>> used {{i, j}};
                    bool found = backtrack(board, word, 1, used, i, j);
                    if (found) return true;
                }
            }
        }
        return false;
    }

    bool backtrack(const vector<vector<char>>& board, const string& word, size_t index, set<pair<size_t, size_t>>& used, size_t i, size_t j) {
        if (index == word.size()) return true;

        if (i > 0) {
            if (!used.contains({i-1, j}) && board[i-1][j] == word.at(index)) {
                used.insert({i-1, j});
                bool found = backtrack(board, word, index+1, used, i-1, j);
                if (found) {
                    return true;
                } else {
                    used.erase({i-1, j});
                }
            }
        }

        if (i < board.size()-1) {
            if (!used.contains({i+1, j}) && board[i+1][j] == word.at(index)) {
                used.insert({i+1, j});
                bool found = backtrack(board, word, index+1, used, i+1, j);
                if (found) {
                    return true;
                } else {
                    used.erase({i+1, j});
                }
            }
        }

        if (j > 0) {
            if (!used.contains({i, j-1}) && board[i][j-1] == word.at(index)) {
                used.insert({i, j-1});
                bool found = backtrack(board, word, index+1, used, i, j-1);
                if (found) {
                    return true;
                } else {
                    used.erase({i, j-1});
                }
            }
        }

        if (j < board[i].size()-1) {
            if (!used.contains({i, j+1}) && board[i][j+1] == word.at(index)) {
                used.insert({i, j+1});
                bool found = backtrack(board, word, index+1, used, i, j+1);
                if (found) {
                    return true;
                } else {
                    used.erase({i, j+1});
                }
            }
        }

        return false;
    }
};
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