<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 {
    vector<vector<int>> memo;
    set<pair<int, int>> visited;
    int ans;
    int dfs(vector<vector<int>>& grid, int row, int col, int n, int m){
        if(row > n-1 || col > m -1 || row < 0 || col < 0) return 0;
        if(grid[row][col] == 1 || visited.find({row, col}) != visited.end()) return 1;
        if(memo[row][col] != -1) return memo[row][col];
        visited.insert({row ,col});
        return memo[row][col] = min(dfs(grid, row - 1, col, n , m), min(dfs(grid, row + 1, col, n, m), min(dfs(grid, row, col - 1, n, m), dfs(grid, row, col + 1, n, m))));

    }
public:
    int closedIsland(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid[0].size();
        memo = vector<vector<int>>(n , vector<int>(m, -1));
        visited.clear();
        ans = 0;
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                if(grid[i][j] == 0 && visited.find({i, j}) == visited.end())
                    ans += dfs(grid, i, j, n, m);
        return ans;
    }
};
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