<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 {
    vector<pair<int, int>> DIRS = {{1,0}, {-1,0}, {0,1}, {0,-1}};
public:
    // checks if indices are within given bounds
    // fact: if a cell has an out of bounds neighbour then is must be on the edge
    //       use this to determine if O region is capturable
    bool isInBounds(int i, int j, int rows, int cols) {
        return i >= 0 && j >= 0 && i < rows && j < cols;
    }

    // Use 'A' to mark visited 'O'
    void replaceCells(vector<vector<char>>& board, int i, int j, char target, char replace) {
        int rows = board.size();
        int cols = board[0].size();
        if (!isInBounds(i, j, rows, cols)) return;
        if (board[i][j] != target) return;

        board[i][j] = replace;
        for (auto& [x, y] : DIRS) {
            replaceCells(board, i+x, j+y, target, replace);
        }
    }

    void solve(vector<vector<char>>& board) {
        for (int i = 0; i < board.size(); ++i) {
            if (board[i][0] == 'O') {
                replaceCells(board, i, 0, 'O', 'A');
            }
            if (board[i][board[0].size()-1] == 'O') {
                replaceCells(board, i, board[0].size()-1, 'O', 'A');
            }
        }
    
        for (int j = 0; j < board[0].size(); ++j) {
            if (board[0][j] == 'O') {
                replaceCells(board, 0, j, 'O', 'A');
            }
            if (board[board.size()-1][j] == 'O') {
                replaceCells(board, board.size()-1, j, 'O', 'A');
            }
        }

        for (int i = 0; i < board.size(); ++i) {
            for (int j = 0; j < board[i].size(); ++j) {
                if (board[i][j] == 'O') {
                    replaceCells(board, i, j, 'O', 'X');
                }
            }
        }
        // fix all non capturable 'O' regions
        for (int i = 0; i < board.size(); ++i) {
            for (int j = 0; j < board[i].size(); ++j) {
                if (board[i][j] == 'A') {
                    replaceCells(board, i, j, 'A', 'O');
                }
            }
        }
    }
};
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