<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, m;
    bool mark[110][110];
    vector<vector<int>> g;
    

    bool free(int x, int y){
      return x>=0 && x<n && y>=0 && y<m && !mark[x][y] && g[x][y]==0;
    }

    void dfs(int x, int y){
        mark[x][y] = true;
       if(free(x+1,y)) dfs(x+1,y);
       if(free(x-1,y)) dfs(x-1,y);
       if(free(x,y+1)) dfs(x,y+1);
       if(free(x,y-1)) dfs(x,y-1);
    }
  
    int closedIsland(vector<vector<int>>& grid) {
        n = grid.size(),m = grid[0].size();
        g = grid;
        int cnt = 0;

        for(int i = 0; i < n; i++){
            if(mark[i][0] != true && g[i][0] == 0) dfs(i,0);
            if(mark[i][m-1] != true && g[i][m-1] == 0) dfs(i,m-1);
        }
        for(int j = 0; j < m; j++){
            if(mark[0][j] != true && g[0][j] == 0) dfs(0,j);
            if(mark[n-1][j] != true && g[n-1][j] == 0) dfs(n-1,j);
        }
        
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(!mark[i][j] && g[i][j]==0){
                     
                        cnt++;
                        dfs(i,j);
                }
            
            }
        }
     return cnt;     
    }   
};
 
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