<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:
    // directions 4 connected
    const vector<pair<int, int>> dirVec = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};

    void bfs(queue<pair<int,int>>&q, vector<vector<int>>& grid) {
        while (q.size()) {
            auto curr = q.front();
            q.pop();

            for (auto& d : dirVec) {
                int ptX = d.first + curr.first;
                int ptY = d.second + curr.second;

                // overflow
                if (ptX < 0 || ptY < 0 || ptX >= grid.size() ||
                    ptY >= grid[0].size())
                    continue;

                if (grid[ptX][ptY] == 0) {
                    grid[ptX][ptY] = 1;
                    q.push({ptX, ptY});
                }
            }
        }
    }

    int closedIsland(vector<vector<int>>& grid) {
        // make all edge 0s -> 1

        int m = grid.size();
        int n = grid[0].size();
        queue<pair<int,int>> q;

        for (int i = 0; i < m; ++i) {
            if (grid[i][0] == 0) {
                q.push({i,0});
            }
            if (grid[i][n - 1] == 0) {
                q.push({i,n-1});
            }
        }
        for (int i = 0; i < n; ++i) {
            if (grid[0][i] == 0) {
                q.push({0,i});
            }
            if (grid[m - 1][i] == 0) {
                q.push({m-1,i});
            }
        }
        bfs(q, grid);
        q = {};
        int cnt = 0;
        //count all islands
        for(int i = 1; i < m-1; ++i){
            for(int j = 1; j < n-1; ++j){
                if(grid[i][j] == 0){
                    q.push({i,j});
                    bfs(q,grid);
                    q = {};
                    cnt++;
                }
            }
        }
        return cnt;
    }
};
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