<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) {
        constexpr array<array<int,2>,4> offsets{{{-1,0},{1,0},{0,-1},{0,1}}};
        int m=heightMap.size(), n=heightMap[0].size();
        vector<vector<int>> maxh(m,vector<int>(n,INT_MAX));
        vector<vector<bool>> seen(m,vector<bool>(n,false));
        queue<pair<int,int>> q;
        
        for(int i=0; i<n; i++){
            q.push(make_pair(0,i));
            q.push(make_pair(m-1,i));
            maxh[0][i] = heightMap[0][i];
            maxh[m-1][i] = heightMap[m-1][i];
            seen[0][i] = true;
            seen[m-1][i] = true;
        }
        for(int i=1; i<m-1; i++){
            q.push(make_pair(i,0));
            q.push(make_pair(i,n-1));
            maxh[i][0] = heightMap[i][0];
            maxh[i][n-1] = heightMap[i][n-1];
            seen[i][0] = true;
            seen[i][n-1] = true;
        }
        /*
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                if(i==0||i==m-1||j==0||j==n-1){
                    q.push(make_pair(i,j));
                    maxh[i][j] = heightMap[i][j];
                    seen[i][j] = true;
                }
            }
        }*/
        while(!q.empty()){
            auto t=q.front();
            q.pop();
            seen[t.first][t.second] = false;
            for(auto [row,col]: offsets){
                row += t.first;
                col += t.second;
                if(row<1 || row>=m-1 || col<1 || col>=n-1) continue;
                if(maxh[t.first][t.second]<maxh[row][col]){
                    // update
                    maxh[row][col] = max(maxh[t.first][t.second], heightMap[row][col]);
                    if(!seen[row][col]){
                        seen[row][col] = true;
                        q.push(make_pair(row,col));
                    }
                }
            }
        }
        int res=0;
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                res += maxh[i][j] - heightMap[i][j];
            }
        }
        return res;

    }
};
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