<p>You are given an <code>m x n</code> binary grid <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water. An <strong>island</strong> is a maximal <strong>4-directionally</strong> (horizontal or vertical) connected group of <code>1</code>&#39;s.</p>

<p>The grid is said to be <strong>connected</strong> if we have <strong>exactly one island</strong>, otherwise is said <strong>disconnected</strong>.</p>

<p>In one day, we are allowed to change <strong>any </strong>single land cell <code>(1)</code> into a water cell <code>(0)</code>.</p>

<p>Return <em>the minimum number of days to disconnect the grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]

<strong>Output:</strong> 2
<strong>Explanation:</strong> We need at least 2 days to get a disconnected grid.
Change land grid[1][1] and grid[0][2] to water and get 2 disconnected island.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land2.jpg" style="width: 404px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [[1,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Grid of full water is also disconnected ([[1,1]] -&gt; [[0,0]]), 0 islands.
</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;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
private:
    // Directions for adjacent cells: right, left, down, up
    const vector<vector<int>> DIRECTIONS = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};

public:
    int minDays(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();

        // Count initial islands
        int initialIslandCount = countIslands(grid);

        // Already disconnected or no land
        if (initialIslandCount != 1) {
            return 0;
        }

        // Try removing each land cell
        for (int row = 0; row < rows; row++) {
            for (int col = 0; col < cols; col++) {
                if (grid[row][col] == 0) continue;  // Skip water

                // Temporarily change to water
                grid[row][col] = 0;
                int newIslandCount = countIslands(grid);

                // Check if disconnected
                if (newIslandCount != 1) return 1;

                // Revert change
                grid[row][col] = 1;
            }
        }

        return 2;
    }

private:
    int countIslands(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();
        vector<vector<bool>> visited(rows, vector<bool>(cols, false));
        int islandCount = 0;

        // Iterate through all cells
        for (int row = 0; row < rows; row++) {
            for (int col = 0; col < cols; col++) {
                // Found new island
                if (!visited[row][col] && grid[row][col] == 1) {
                    exploreIsland(grid, row, col, visited);
                    islandCount++;
                }
            }
        }
        return islandCount;
    }

    // Helper method to explore all cells of an island
    void exploreIsland(vector<vector<int>>& grid, int row, int col,
                       vector<vector<bool>>& visited) {
        visited[row][col] = true;

        // Check all adjacent cells
        for (const auto& direction : DIRECTIONS) {
            int newRow = row + direction[0];
            int newCol = col + direction[1];
            // Explore if valid land cell
            if (isValidLandCell(grid, newRow, newCol, visited)) {
                exploreIsland(grid, newRow, newCol, visited);
            }
        }
    }

    bool isValidLandCell(const vector<vector<int>>& grid, int row, int col,
                         const vector<vector<bool>>& visited) {
        int rows = grid.size();
        int cols = grid[0].size();
        // Check bounds, land, and not visited
        return row >= 0 && col >= 0 && row < rows && col < cols &&
               grid[row][col] == 1 && !visited[row][col];
    }
};
20540