<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:
vector<int> p;
    vector<int> r;

    int findp(int i, vector<int>& p) {
        if (i == p[i])
            return i;
        return p[i] = findp(p[i], p);
    }

    void uni(int i, int j, vector<int>& p, vector<int>& r) {
        int ip = findp(i, p);
        int jp = findp(j, p);
        if (ip == jp)
            return;
        if (r[ip] < r[jp]) {
            p[ip] = jp;
        } else if (r[ip] > r[jp]) {
            p[jp] = ip;
        } else {
            p[jp] = ip;
            r[ip]++;
        }
    }

    bool v(int x, int y, int m, int n) {
        return x >= 0 && y >= 0 && x < m && y < n;
    }
    void vini(vector<vector<int>>& grid, int x, int y){
        if(x < 0 || y < 0 || x >= grid.size() || y >= grid[0].size()) return;
        if(!grid[x][y]){
            grid[x][y] = 1;
            vini(grid, x+1, y);
            vini(grid, x-1, y);
            vini(grid, x, y+1);
            vini(grid, x, y-1);
        }
    }
    int closedIsland(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        for(int i = 0; i < m; i++){
            if(!grid[i][0]) vini(grid, i, 0);
            if(!grid[i][n-1]) vini(grid, i, n-1);
        }
        for(int i = 0; i < n; i++){
            if(!grid[0][i]) vini(grid, 0, i);
            if(!grid[m-1][i]) vini(grid, m-1, i);
        }
        p.resize(m * n, 0);
        r.resize(m * n, 0);
        for (int i = 0; i < m * n; i++) {
            p[i] = i;
        }
        int c = 0;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 0) {
                    c++;
                    int Node1 = i * n + j;
                    vector<int> dr = {-1, 0, +1, 0};
                    vector<int> dc = {0, -1, 0, +1};
                    for (int k = 0; k < dr.size(); k++) {
                        int nrow = i + dr[k];
                        int ncol = j + dc[k];
                        if (v(nrow, ncol, m, n) && grid[nrow][ncol] == 0) {
                            int Node2 = nrow * n + ncol;
                            if (findp(Node1, p) != findp(Node2, p)) {
                                c--;
                                uni(Node1, Node2, p, r);
                            }
                        }
                    }
                }
            }
        }
        return c;
        
    }
};
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