<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>

#define piii pair<int,pair<int,int>>

class Comp{
public:
    bool operator()(piii& a, piii& b){
        return a.first>b.first;
    }

};

class Solution {
public:
    int trapRainWater(vector<vector<int>>& heightMap) {
        int res=0;
        
        int n=heightMap.size(), m=heightMap[0].size();
        vector<vector<bool>> vis(n, vector<bool> (m, false));
        priority_queue<piii, vector<piii>, Comp> pq;
        for(int i=0;i<n;i++){
            vis[i][0]=true;
            pq.push({heightMap[i][0], {i,0}});
            vis[i][m-1]=true;
            pq.push({heightMap[i][m-1], {i,m-1}});
        }

        for(int i=1;i<m-1;i++){
            vis[0][i]=true;
            pq.push({heightMap[0][i], {0,i}});
            vis[n-1][i]=true;
            pq.push({heightMap[n-1][i], {n-1,i}});
        }

        while(!pq.empty()){
            piii tmp=pq.top(); pq.pop();
            int ht=tmp.first, r=tmp.second.first, c=tmp.second.second;

            vector<int> adj={0,-1,0,1,0};
            for(int i=0;i<4;i++){
                int adj_r=r+adj[i], adj_c=c+adj[i+1];
                if(adj_r<0 || adj_r>=n || adj_c<0 || adj_c>=m || vis[adj_r][adj_c])  continue;

                vis[adj_r][adj_c]=true;
                int adj_ht=heightMap[adj_r][adj_c];
                if(adj_ht<ht){
                    res+=ht-adj_ht;
                    pq.push({ht, {adj_r, adj_c}});
                }
                else{
                    pq.push({adj_ht, {adj_r, adj_c}});
                }
            }
        }

        return res;
    }
};
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