<p>You are given an <code>m x n</code> integer matrix <code>grid</code>, and three integers <code>row</code>, <code>col</code>, and <code>color</code>. Each value in the grid represents the color of the grid square at that location.</p>

<p>Two squares are called <strong>adjacent</strong> if they are next to each other in any of the 4 directions.</p>

<p>Two squares belong to the same <strong>connected component</strong> if they have the same color and they are adjacent.</p>

<p>The <strong>border of a connected component</strong> is all the squares in the connected component that are either adjacent to (at least) a square not in the component, or on the boundary of the grid (the first or last row or column).</p>

<p>You should color the <strong>border</strong> of the <strong>connected component</strong> that contains the square <code>grid[row][col]</code> with <code>color</code>.</p>

<p>Return <em>the final grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> grid = [[1,1],[1,2]], row = 0, col = 0, color = 3
<strong>Output:</strong> [[3,3],[3,2]]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> grid = [[1,2,2],[2,3,2]], row = 0, col = 1, color = 3
<strong>Output:</strong> [[1,3,3],[2,3,3]]
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> grid = [[1,1,1],[1,1,1],[1,1,1]], row = 1, col = 1, color = 2
<strong>Output:</strong> [[2,2,2],[2,1,2],[2,2,2]]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j], color &lt;= 1000</code></li>
	<li><code>0 &lt;= row &lt; m</code></li>
	<li><code>0 &lt;= col &lt; n</code></li>
</ul>

class Solution:
    def colorBorder(self, grid: List[List[int]], row: int, col: int, color: int) -> List[List[int]]:
        rows, cols = len(grid), len(grid[0])
        directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]
        prevColor = grid[row][col]
        visited = set()
        border = []
        
        # Check if the position is within the grid
        def is_valid(r, c):
            return 0 <= r < rows and 0 <= c < cols
        
        # DFS to explore the connected component and find the border cells
        def dfs(r, c):
            visited.add((r, c))
            is_border = False
            
            for dr, dc in directions:
                nr, nc = r + dr, c + dc
                if not is_valid(nr, nc) or grid[nr][nc] != prevColor:
                    is_border = True
                elif (nr, nc) not in visited:
                    dfs(nr, nc)
            
            # Mark the cell as border if it's either on the boundary or adjacent to a different color
            if is_border or r in [0, rows - 1] or c in [0, cols - 1]:
                border.append((r, c))
        
        # Start DFS from the given starting point
        dfs(row, col)
        
        # Color the border cells
        for r, c in border:
            grid[r][c] = color
        
        return grid

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