<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 minDays(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid.front().size();
        vector<pair<int, int>> step = {
            { 0, -1 },
            { 0, 1 },
            { -1, 0 },
            { 1, 0 }
        };
        auto is_between = [](int x, int lim) -> bool {
            return x >= 0 && x < lim;
        };
        auto check = [&](int x, int y) -> bool {
            return is_between(x, n) && is_between(y, m) && grid[x][y] == 1;
        };
        map<pair<int, int>, char> dict, used;
        function<void(int, int)> dfs = [&](int x, int y) -> void {
            used[make_pair(x, y)] = 1;
            for (const auto& i : step) {
                if (check(x + i.first, y + i.second) && !used[make_pair(x + i.first, y + i.second)]) {
                    dfs(x + i.first, y + i.second);
                }
            }
        };

        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                if (grid[i][j] == 1) {
                    dict[make_pair(i, j)] = 0;
                }
            }
        }

        auto solve = [&]() -> bool {
            bool is_found = false;
            used = dict;
            for (auto& i : used) {
                assert(grid[i.first.first][i.first.second]);
                if (!i.second) {
                    if (is_found) {
                        return false;
                    }
                    dfs(i.first.first, i.first.second);
                    is_found = true;
                }
            }
            return is_found;
        };

        if (!solve()) {
            return 0;
        }
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                if (grid[i][j]) {
                    grid[i][j] = 0;
                    dict.erase(make_pair(i, j));
                    if (!solve()) {
                        return 1;
                    }
                    grid[i][j] = 1;
                    dict[make_pair(i, j)] = 0;
                }
            }
        }
        return 2;
    }
};
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