<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:
    bool isValid(int x, int y, int n, int m){
        return x>=0 && x<n && y>=0 && y<m;
    }
    void dfs(int x, int y, vector<vector<int>>& grid){
        int n = grid.size();
        int m = grid[0].size();
        grid[x][y]=1;
        vector<int> dx = {-1, 0, 1, 0};
        vector<int> dy = {0, -1, 0, 1};
        for(int i=0; i<4; i++){
            int newx = x+dx[i];
            int newy = y+dy[i];
            if(isValid(newx, newy, n, m) && grid[newx][newy]==0){
                dfs(newx, newy, grid);
            }
        }
    }
    int closedIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        for(int i=0; i<n; i++){
            if(grid[i][0]==0)
            dfs(i, 0, grid);
            if(grid[i][m-1]==0)
            dfs(i, m-1, grid);
        }
        for(int j=0; j<m; j++){
            if(grid[0][j]==0)
            dfs(0, j, grid);
            if(grid[n-1][j]==0)
            dfs(n-1, j, grid);
        }
        int cnt = 0;
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++){
                if(grid[i][j]==0){
                    dfs(i, j, grid);
                    cnt++;
                }
            }
        }
        return cnt;
    }
};
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