<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 info
{
    public:
    int height;
    int row;
    int col;
};


class cmp
{
    public:
    bool operator()(info& a,info& b)
    {
        return a.height>b.height;
    }
};

class Solution {
public:
    int trapRainWater(vector<vector<int>>& heightMap) {
        int m=heightMap.size();
        int n=heightMap[0].size();

        map<pair<int,int>,bool>visited;
        priority_queue<info,vector<info>,cmp>minHeap;

        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 )
                {
                    visited[{i,j}]=true;
                    minHeap.push({heightMap[i][j],i,j});
                }
            }
        }

        int water=0;
        int maxBndHeight=0;
        

        while(!minHeap.empty())
        {
            auto top=minHeap.top();
            minHeap.pop();

            int topHeight=top.height;
            int topRow=top.row;
            int topCol=top.col;

            maxBndHeight=max(maxBndHeight,topHeight);

            int dx[4]={1,-1,0,0};
            int dy[4]={0,0,1,-1};

            for(int i=0;i<4;i++)
            {
                int newX=topRow+dx[i];
                int newY=topCol+dy[i];

                if(newX>=0 && newX<m && newY>=0 && newY<n && !visited[{newX,newY}])
                {
                    visited[{newX,newY}]=true;
                    if(heightMap[newX][newY]<maxBndHeight)
                    {
                        water+=maxBndHeight-heightMap[newX][newY];  
                    }
                    minHeap.push({heightMap[newX][newY],newX,newY});
                }
            }
        }

         return water;
    }
};
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