<p>Given a 2D&nbsp;<code>grid</code> consists of <code>0s</code> (land)&nbsp;and <code>1s</code> (water).&nbsp; An <em>island</em> is a maximal 4-directionally connected group of <code><font face="monospace">0</font>s</code> and a <em>closed island</em>&nbsp;is an island <strong>totally</strong>&nbsp;(all left, top, right, bottom) surrounded by <code>1s.</code></p>

<p>Return the number of <em>closed islands</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/31/sample_3_1610.png" style="width: 240px; height: 120px;" /></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1,1,0],[1,0,0,0,0,1,1,0],[1,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,1],[1,1,1,1,1,1,1,0]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
Islands in gray are closed because they are completely surrounded by water (group of 1s).</pre>

<p><strong class="example">Example 2:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/31/sample_4_1610.png" style="width: 160px; height: 80px;" /></p>

<pre>
<strong>Input:</strong> grid = [[0,0,1,0,0],[0,1,0,1,0],[0,1,1,1,0]]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1,1],
&nbsp;              [1,0,0,0,0,0,1],
&nbsp;              [1,0,1,1,1,0,1],
&nbsp;              [1,0,1,0,1,0,1],
&nbsp;              [1,0,1,1,1,0,1],
&nbsp;              [1,0,0,0,0,0,1],
               [1,1,1,1,1,1,1]]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= grid.length, grid[0].length &lt;= 100</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;=1</code></li>
</ul>

class Solution {
// private:
//     void dfs(vector<vector<int>>& grid, int r, int c) {
//       if (r < 0 || r >= grid.size() || c < 0 || c >= grid[0].size() || grid[r][c] != 0) {
//         return;
//       }
//       grid[r][c] = 2;
//       dfs(grid, r + 1, c);
//       dfs(grid, r - 1, c);
//       dfs(grid, r, c + 1);
//       dfs(grid, r, c - 1);
//     }  
// public:
//     int closedIsland(vector<vector<int>>& grid) {
//       vector<vector<int>> land_e;
//       int rows = grid.size();
//       int cols = grid[0].size();
//       for (int r = 0; r < rows; r++) {
//         if (grid[r][0] == 0) land_e.push_back({r, 0});
//         if (grid[r][cols-1] == 0) land_e.push_back({r, cols - 1});
//       }

//       for (int c = 1; c < cols - 1; c++) {
//          if (grid[0][c] == 0) land_e.push_back({0, c});
//          if (grid[rows - 1][c] == 0) land_e.push_back({rows - 1, c});
//       }

//       for (auto l : land_e) {
//         if (grid[l[0]][l[1]] != 0) continue;
//         dfs(grid, l[0], l[1]);
//       }

//       int num_islands = 0;
//       for (int r = 1; r < rows; r++) {
//         for (int c = 1; c < cols; c++) {
//           if (grid[r][c] != 0) continue;
//           dfs(grid, r, c);
//           num_islands += 1;
//         }
//       }
//       return num_islands; 
//     }


    public:
    int closedIsland(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        int count = 0;
        vector<vector<bool>> visit(m, vector<bool>(n));
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 0 && !visit[i][j] && dfs(i, j, m, n, grid, visit)) {
                    count++;
                }
            }
        }
        return count;
    }

    bool dfs(int x, int y, int m, int n, vector<vector<int>>& grid, vector<vector<bool>>& visit) {
        if (x < 0 || x >= m || y < 0 || y >= n) {
            return false;
        }
        if (grid[x][y] == 1 || visit[x][y]) {
            return true;
        }

        visit[x][y] = true;
        bool isClosed = true;
        vector<int> dirx {0, 1, 0, -1};
        vector<int> diry {-1, 0, 1, 0};

        for (int i = 0; i < 4; i++) {
            int r = x + dirx[i];
            int c = y + diry[i];
            if (!dfs(r, c, m, n, grid, visit)) {
                isClosed = false;
            }
        }

        return isClosed;
    }
};
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