<p>You are given an <code>m x n</code> matrix <code>board</code> containing <strong>letters</strong> <code>&#39;X&#39;</code> and <code>&#39;O&#39;</code>, <strong>capture regions</strong> that are <strong>surrounded</strong>:</p>

<ul>
	<li><strong>Connect</strong>: A cell is connected to adjacent cells horizontally or vertically.</li>
	<li><strong>Region</strong>: To form a region <strong>connect every</strong> <code>&#39;O&#39;</code> cell.</li>
	<li><strong>Surround</strong>: The region is surrounded with <code>&#39;X&#39;</code> cells if you can <strong>connect the region </strong>with <code>&#39;X&#39;</code> cells and none of the region cells are on the edge of the <code>board</code>.</li>
</ul>

<p>A <strong>surrounded region is captured</strong> by replacing all <code>&#39;O&#39;</code>s with <code>&#39;X&#39;</code>s in the input matrix <code>board</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = [[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;O&quot;,&quot;O&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;X&quot;,&quot;O&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;O&quot;,&quot;X&quot;,&quot;X&quot;]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;O&quot;,&quot;X&quot;,&quot;X&quot;]]</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/19/xogrid.jpg" style="width: 367px; height: 158px;" />
<p>In the above diagram, the bottom region is not captured because it is on the edge of the board and cannot be surrounded.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = [[&quot;X&quot;]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[&quot;X&quot;]]</span></p>
</div>

<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;= 200</code></li>
	<li><code>board[i][j]</code> is <code>&#39;X&#39;</code> or <code>&#39;O&#39;</code>.</li>
</ul>

class Solution {
public: 
    bool isSafe(int i, int j, int m, int n) {
        if(i<0 or j<0 or i>=m or j>=n) return false;
        return true;
   }
    void dfs(int i, int j, int m, int n, vector<vector<char>>&grid) {
        if(grid[i][j] == 'X') return;
        grid[i][j] = 'X';
        vector<pair<int, int>> directions =  {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
        for(int dir = 0; dir<directions.size(); dir++) {
                    int newX = directions[dir].first + i;
                    int newY = directions[dir].second + j;
                    if(isSafe(newX, newY, m, n)) {
                            dfs(newX, newY, m, n, grid);
                    }
                }

    }
    void fillBoundaries(int i, int j, int m, int n, vector<vector<char>>&board) {
        if(isSafe(i, j, m, n)) {
            if(board[i][j] == 'X' or board[i][j] == '1') return;
            board[i][j] = '1';
             vector<pair<int, int>> directions =  {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
            for(int dir = 0; dir<directions.size(); dir++) {
                        int newX = directions[dir].first+i;
                        int newY = directions[dir].second+j;
                        fillBoundaries(newX, newY, m, n, board);
                }
        }
    }
    void solve(vector<vector<char>>& board) {
        int m = board.size();
        int n = board[0].size();
        for(int j = 0; j<n; j++) {
            fillBoundaries(0, j, m, n,board);
            fillBoundaries(m-1, j, m, n, board);
        }

        for(int i = 0; i<m; i++) {
            fillBoundaries(i, 0, m, n, board);
            fillBoundaries(i, n-1, m, n, board);
        }
       
        for(int i = 0; i<m; i++) {
            for(int j = 0; j<n; j++) {
                if(board[i][j] == 'O') {
                    dfs(i, j, m, n, board);
                }
            }
        }
        for(int i = 0; i<m; i++) {
            for(int j =0 ; j<n; j++) {
                if(board[i][j] == '1') board[i][j] = 'O';
            }
        }
    }
};
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