<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:
    def solve(self, board: List[List[str]]) -> None:
        """
        Do not return anything, modify board in-place instead.
        """
        # mark 'O' cells on the edges of the board as visited
        # so we know to backtrack from these edged '0' cells when we encounter them
        # in a DFS

        # then, we iterate through cells of the board again
        # and we do dfs and mark every non-visited '0' cell as 'X'

        ROWS = len(board)
        COLS = len(board[0])
        visited = set()

        def isSurrounded(row, col):
            print("hi", row, col)
            if (
                board[row][col + 1] == 'X' or
                board[row][col - 1] == 'X' or
                board[row + 1][col] == 'X' or
                board[row - 1][col] == 'X'
            ):
                print("t", row, col)
                return True
            return False

        def dfs(row, col, isEdged):
            # backtrack if cell is out of bounds
            # or if cell is 'X'
            # or if cell is visited
            if (
                row < 0 or
                col < 0 or
                row >= ROWS or
                col >= COLS or
                board[row][col] == 'X' or
                (row, col) in visited
            ):
                return
            
            # mark region as visited
            visited.add((row, col))

            # mark region as surrounded if region is not in edges
            # and if region is not a part of a region that is edged
            # and if region is surrounded
            if (
                (row > 0 and row < ROWS - 1) and
                (col > 0 and col < COLS - 1) and
                (not isEdged) and
                (isSurrounded(row, col))
            ):
                board[row][col] = 'X'

            # traverse all neighbours
            dfs(row, col + 1, isEdged) # right
            dfs(row, col - 1, isEdged) # left
            dfs(row + 1, col, isEdged) # up 
            dfs(row - 1, col, isEdged) # down

        # ROW = 0, ROW - 1
        # iterate through all cells in the top and bottom edges of the board
        for col in range(COLS):
            dfs(0, col, True) # top edges of the board
            dfs(ROWS - 1, col, True) # bottom edges of the board

        # COL = 0, COL - 1
        # iterate through all cells in the top and bottom edges of the board
        for row in range(ROWS):
            dfs(row, 0, True) # left edges of the board
            dfs(row, COLS - 1, True) # right edges of the board


        # traverse the board again
        # calling dfs on each cell
        for row in range(ROWS):
            for col in range(COLS):
                dfs(row, col, False)
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