<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 calculate(vector<vector<char>>& board, string word, map<pair<int,int>, int>& mp, pair<int,int> curr, int idx) {
        if(curr.first >= board.size() || curr.second>= board[0].size() || idx>= word.length()
            || curr.first < 0 || curr.second < 0) {
            return false;
        }
        if(mp.find(curr) != mp.end() && mp[curr] == 1) {
            return false;
        }
        mp[curr] = 1;
        if(word[idx] != board[curr.first][curr.second]) {
            mp[curr] = -1;
            return false;
        }
        if(word[idx] == board[curr.first][curr.second] && idx == word.length()-1) {
            return true;
        }
        bool right = calculate(
            board,
            word,
            mp,
            make_pair(curr.first, curr.second+1),
            idx+1
        );
        if(right) {
            return true;
        }
        bool down = calculate(
            board,
            word,
            mp,
            make_pair(curr.first+1, curr.second),
            idx+1
        );
        if(down) {
            return true;
        }
        bool left = calculate(
            board,
            word,
            mp,
            make_pair(curr.first, curr.second-1),
            idx+1
        );
        if(left) {
            return true;
        }
        bool up = calculate(
            board,
            word,
            mp,
            make_pair(curr.first-1, curr.second),
            idx+1
        );
        if(up) {
            return true;
        }
        mp[curr] = -1;
        return false;
    }
    bool exist(vector<vector<char>>& board, string word) {
        map<pair<int,int>, int> mp;
        for(int i=0; i<board.size(); i++) {
            for(int j=0; j<board[0].size(); j++) {
                bool res = calculate(
                    board,
                    word,
                    mp,
                    make_pair(i,j),
                    0
                );
                if(res) {
                    return true;
                }
            }
        }
        return false; 
    }
};
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