<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<vector<int>, vector<vector<int>>, greater<vector<int>>> pq;
        vector<vector<int>> vis(n, vector<int>(m,false));

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

        vector<vector<int>> dir = {{1,0},{0,1} ,{-1,0},{0,-1}};
        int water = 0;
        
        while(!pq.empty()) {
            int h = pq.top()[0];
            int r = pq.top()[1];
            int c = pq.top()[2];
            pq.pop();

            for(int i=0; i<4; i++) {
                int nr = r + dir[i][0];
                int nc = c + dir[i][1];

                if (nr>=0 && nr<n && nc>=0 && nc<m && !vis[nr][nc]) {
                    vis[nr][nc] = true;
                    if (heightMap[nr][nc] > h) {
                        pq.push({heightMap[nr][nc], nr, nc});
                    } else if (heightMap[nr][nc] == h) {
                        pq.push({h, nr, nc});
                    } else {
                        water += h-heightMap[nr][nc];
                        pq.push({h, nr, nc});
                    }
                }
            }
        }

        return water;
    }
};
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