<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:
    void dfs(vector<vector<int>>& grid, int m, int n, int i, int j, bool& isBoundary) {
        grid[i][j] = -1;
        if (!isBoundary && i == 0 || j == 0 || i == m - 1 || j == n - 1)
            isBoundary = true;
        if (i + 1 < m && !grid[i+1][j])
            dfs(grid, m, n, i+1, j, isBoundary);
        if (i - 1 >= 0 && !grid[i-1][j])
            dfs(grid, m, n, i - 1, j, isBoundary);
        if (j + 1 < n && !grid[i][j+1])
            dfs(grid, m, n, i, j + 1, isBoundary);
        if (j - 1 >= 0 && !grid[i][j-1])
            dfs(grid, m, n, i, j-1, isBoundary);
    }
    
    void bfs(vector<vector<int>>& grid, int m, int n, int i, int j, bool& isBoundary) {
        queue<pair<int, int>>q;
        grid[i][j] = -1;
        q.push({i,j});
        
        while(!q.empty()) {
            i = q.front().first;
            j = q.front().second;
            if (!isBoundary && i == 0 || j == 0 || i == m - 1 || j == n - 1)
                isBoundary = true;
            if (i + 1 < m && !grid[i+1][j]) {
                q.push({i+1, j});
                grid[i+1][j] = true;
            }
            if (i - 1 >= 0 && !grid[i-1][j]) {
                q.push({i-1,j});
                grid[i-1][j] = true;
            }
            if (j + 1 < n && !grid[i][j+1]) {
                q.push({i, j+1});
                grid[i][j+1] = true;
            }
            if (j - 1 >= 0 && !grid[i][j-1]) {
                q.push({i, j-1});
                grid[i][j-1] = true;
            }
            q.pop();
        }
        
    }
    int closedIsland(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        int closedIslands = 0;
        for(int i = 0; i < m; ++i) {
            for(int j = 0; j < n; ++j) {
                bool isBoundary = false;

                if (grid[i][j] == 0) {
                    bfs(grid, m, n, i, j, isBoundary);
                    if (!isBoundary)
                        closedIslands++;
                }
            }
        }
        return closedIslands;
    }
};
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