<p>Given an <code>m x n</code> integer matrix <code>heightMap</code> representing the height of each unit cell in a 2D elevation map, return <em>the volume of water it can trap after raining</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/trap1-3d.jpg" style="width: 361px; height: 321px;" />
<pre>
<strong>Input:</strong> heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> After the rain, water is trapped between the blocks.
We have two small ponds 1 and 3 units trapped.
The total volume of water trapped is 4.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/trap2-3d.jpg" style="width: 401px; height: 321px;" />
<pre>
<strong>Input:</strong> heightMap = [[3,3,3,3,3],[3,2,2,2,3],[3,2,1,2,3],[3,2,2,2,3],[3,3,3,3,3]]
<strong>Output:</strong> 10
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == heightMap.length</code></li>
	<li><code>n == heightMap[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= heightMap[i][j] &lt;= 2 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int dir[4][2] = {-1, 0, 0, 1, 1, 0, 0, -1};
    class myCompare{
        public:
        bool operator()(vector<int>& lhs, vector<int>& rhs){
            return lhs[2]>rhs[2];
        }
    };
    int n = 0;
    int m = 0;
    vector<vector<int>> v; // 0, not visited
    int trapRainWater(vector<vector<int>>& heightMap) {
        n = heightMap.size();
        m = heightMap[0].size();
        v.resize(n, vector<int>(m, 0));

        priority_queue<vector<int>, vector<vector<int>>, myCompare> minq;

        for(int i = 0; i < n; i++){
            minq.push({i, 0, heightMap[i][0]});
            minq.push({i, m-1, heightMap[i][m-1]});
            v[i][0]=1;
            v[i][m-1]=1;
        }
        for(int j = 0; j < m; j++){
            minq.push({0, j, heightMap[0][j]});
            minq.push({n-1, j, heightMap[n-1][j]});
            v[0][j]=1;
            v[n-1][j]=1;
        }

        int res = 0;
        while(!minq.empty()){
            vector<int> node = minq.top(); minq.pop();
            int x = node[0];
            int y = node[1];
            int h = node[2];
            res += h-heightMap[x][y];
            for(int i = 0; i < 4; i++){
                int nx = x + dir[i][0];
                int ny = y + dir[i][1];
                if(nx<0 || nx>=n || ny<0 || ny>=m) continue;
                if(v[nx][ny] != 0) continue;
                v[nx][ny]=1;
                minq.push({nx, ny, max(h, heightMap[nx][ny])});
            }
        }
        return res;
    }
};
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