<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.
        """
        # iterate looking for O
        # dfs from O looking for edge
        #   convert each O to X
        #   if at the end no edge is found
        #       revert X to O
        DIRECTIONS = [(1, 0), (0, 1), (-1, 0), (0, -1)]
        M = len(board)
        N = len(board[0])

        # dfs through an island
        #   set each cell to X
        #   on return if an edge was found set it to N (so we don't check the island again)
        def findEdge(i, j):
            nonlocal edgeFound
            board[i][j] = "E"
            for di, dj in DIRECTIONS:
                ni = i + di
                nj = j + dj
                if ni < 0 or ni >= M or nj < 0 or nj >= N:
                    edgeFound = True
                elif board[ni][nj] == "O":
                    findEdge(ni, nj)

        def clearRegion(i, j):
            nonlocal edgeFound
            board[i][j] = "N" if edgeFound else "X"
            for di, dj in DIRECTIONS:
                ni = i + di
                nj = j + dj
                if ni >= 0 and ni < M and nj >= 0 and nj < N and board[ni][nj] == "E":
                    clearRegion(ni, nj)

        # search for each island
        edgeFound = False
        for i in range(M):
            for j in range(N):
                if board[i][j] == "O":
                    findEdge(i, j)
                    if edgeFound:
                        clearRegion(i, j)
                        edgeFound = False

        # set all N back to O
        for i in range(M):
            for j in range(N):
                if board[i][j] == "N":
                    board[i][j] = "O"
                elif board[i][j] == "E":
                    board[i][j] = "X"

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