<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 {
public:
    int n;
    int m;
    
    bool bfs(int r, int c, vector<vector<int>>& grid) {
        // Directions for moving up, down, left, right
        vector<pair<int, int>> directions = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}};
        queue<pair<int, int>> q;
        q.push({r, c});
        bool isClosed = true;

        // Mark the current cell as visited
        grid[r][c] = 1;
        
        // BFS to visit all connected 0s
        while (!q.empty()) {
            auto [x, y] = q.front();
            q.pop();
            
            // Explore neighbors in all four directions
            for (auto [dx, dy] : directions) {
                int nx = x + dx;
                int ny = y + dy;
                
                // If we reach the boundary, it's not a closed island
                if (nx < 0 || nx >= n || ny < 0 || ny >= m) {
                    isClosed = false;
                }
                // If the neighbor is an unvisited land (0), add it to the queue
                else if (grid[nx][ny] == 0) {
                    grid[nx][ny] = 1;  // Mark as visited
                    q.push({nx, ny});
                }
            }
        }
        return isClosed;
    }

    int closedIsland(vector<vector<int>>& grid) {
        n = grid.size();
        m = grid[0].size();
        int count = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (grid[i][j] == 0) {
                    if (bfs(i, j, grid)) {
                        count++;  // Increment if the island is closed
                    }
                }
            }
        }
        return count;
    }
};

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