<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 trapRainWater(vector<vector<int>>& heightMap) {
        int n=heightMap.size();
        int m=heightMap[0].size();
        priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
        vector<bool>vis(n*m,false);
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(i==0||j==0||i==n-1||j==m-1){
                    vis[m*i+j]=true;
                    pq.push({heightMap[i][j],m*i+j});
                }
            }
        }
        int trappedWater=0;
        int dr[4]={-1,0,1,0};
        int dc[4]={0,-1,0,1};
        while(!pq.empty()){
            int node=pq.top().second;
            int height=pq.top().first;
            int r=node/m;int c=node%m;
            pq.pop();
            for(int i=0;i<4;i++){
                int nr=r+dr[i];
                int nc=c+dc[i];
                if(nr<0||nc<0||nr==n||nc==m||vis[nr*m+nc])continue;
                trappedWater+=max(0,height-heightMap[nr][nc]);
                pq.push({max(height,heightMap[nr][nc]),nr*m+nc});
                vis[nr*m+nc]=true;
            }
        }
        return trappedWater;
    }
};
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