<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 {
public:
    int dfs(vector<vector<int>>& grid, int i, int j, vector<vector<bool>>& select) {
        if (i < 0 || i >= grid.size() || j < 0 || j >= grid[0].size() || grid[i][j] == 0 || select[i][j]) {
            return 0;
        }
        int res = 0;
        if (grid[i][j]) {
            res++;
            select[i][j] = true;
        }
        res += dfs(grid, i + 1, j, select);
        res += dfs(grid, i - 1, j, select);
        res += dfs(grid, i, j + 1, select);
        res += dfs(grid, i, j - 1, select);

        return res;
    }

    int minDays(vector<vector<int>>& grid) {
        int count = 0;
        int m = 0, n = 0;
        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j]) {
                    count++;
                    m = i;
                    n = j;
                }
            }
        }

        // printf("%d %d\n", m, n);
        vector<vector<bool>> select(grid.size(), vector<bool>(grid[0].size()));
        if (count != dfs(grid, m, n, select)) {
            return 0;
        }
        if (count <= 1) {
            return count;
        }
        // printf("%d\n", count);

        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j]) {
                    bool left = false, up = false, right = false, down = false;
                    if (i - 1 >= 0 && grid[i - 1][j] == 1) {
                        up = true;
                    } 
                    if (j - 1 >= 0 && grid[i][j - 1] == 1) {
                        left = true;
                    } 
                    if (i + 1 < grid.size() && grid[i + 1][j] == 1) {
                        down = true;
                    } 
                    if (j + 1 < grid[0].size() && grid[i][j + 1] == 1) {
                        right = true;
                    } 
                    // if (left + right + up + down > 2) {
                    //     continue;
                    // }

                    if (up) {
                        vector<vector<bool>> select(grid.size(), vector<bool>(grid[0].size()));
                        select[i - 1][j] = true;
                        if (count - 1 != dfs(grid, i, j, select)) {
                            return 1;
                        }
                    }
                    if (left) {
                        vector<vector<bool>> select(grid.size(), vector<bool>(grid[0].size()));
                        select[i][j - 1] = true;
                        if (count - 1 != dfs(grid, i, j, select)) {
                            return 1;
                        }
                    }
                    if (down) {
                        vector<vector<bool>> select(grid.size(), vector<bool>(grid[0].size()));
                        select[i + 1][j] = true;
                        if (count - 1 != dfs(grid, i, j, select)) {
                            return 1;
                        }
                    }
                    if (right) {
                        vector<vector<bool>> select(grid.size(), vector<bool>(grid[0].size()));
                        select[i][j + 1] = true;
                        if (count - 1 != dfs(grid, i, j, select)) {
                            return 1;
                        }
                    }

                }
            }
        }

        return 2;
    }
};
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