<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>>& vec) {
        int n = vec.size();
        int m = vec[0].size();
        priority_queue<vector<int>> pq;
        vector<vector<bool>> vis(n,vector<bool>(m,0));
        for(int i=0;i<n;i++)
        {
            pq.push({vec[i][0]*-1,i,0});
            pq.push({vec[i][m-1]*-1,i,m-1});
            vis[i][0]=1;
            vis[i][m-1]=1;
        }
        for(int j=1;j<m-1;j++)
        {
            pq.push({vec[0][j]*-1,0,j});
            vis[0][j]=1;
            pq.push({vec[n-1][j]*-1,n-1,j});
            vis[n-1][j] = 1;
        }
        vector<int> moveX = {0,1,0,-1};
        vector<int> moveY = {1,0,-1,0};
        int ans = 0;
        while(!pq.empty())
        {
            int val = pq.top()[0]*-1;
            int y = pq.top()[1];
            int x = pq.top()[2];
            pq.pop();
            for(int i=0;i<4;i++)
            {
                int newX = x+moveX[i];
                int newY = y+moveY[i];
                if(newX>=0 && newX<m && newY>=0 && newY<n && vis[newY][newX]==0)
                {
                    if(val==vec[newY][newX])
                    {
                        vis[newY][newX] = 1;
                        pq.push({val*-1,newY,newX});
                    }
                    else if(val>vec[newY][newX])
                    {
                        ans+=val-vec[newY][newX];
                        vec[newY][newX] = val;
                        vis[newY][newX] = 1;
                        pq.push({val*-1,newY,newX});
                    }
                    else
                    {
                        vis[newY][newX] = 1;
                        pq.push({vec[newY][newX]*-1,newY,newX});
                    }
                }
            }
        }
        return ans;
    }
};
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