<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) {
        priority_queue<vector<int>, vector<vector<int>>, greater<vector<int>>> pq;
        vector<vector<bool>> visited; 
        int rows[] = {0,0,1,-1};
        int cols[] = {1,-1,0,0};

        int r = heightMap.size();
        int c = heightMap[0].size();

        for(int i=0;i<r;i++) {
            visited.push_back({});
            for(int j=0;j<c;j++) {
                visited[i].push_back(false);
            }
        }

        for(int i=0;i<r;i++) {
            pq.push({heightMap[i][0], i, 0});
            pq.push({heightMap[i][c-1], i, c-1});
            visited[i][0] = true;
            visited[i][c-1] = true;
        }

        for(int i=0;i<c;i++) {
            pq.push({heightMap[0][i], 0, i});
            pq.push({heightMap[r-1][i], r-1, i});
            visited[0][i] = true;
            visited[r-1][i] = true;
        }

        int ans = 0;

        while (!pq.empty()) {
            vector<int> v = pq.top();
            int R = v[1];
            int C = v[2];
            int H = v[0];

            pq.pop();

            for(int i=0;i<4;i++) {
                int row = R + rows[i];
                int col = C + cols[i];

                if (row >= 0 && row < r && col >= 0 && col < c) {
                    if (visited[row][col]) {
                        continue;
                    }

                    if (H > heightMap[row][col]) {
                        ans += H - heightMap[row][col];
                    }
                    visited[row][col] = true;
                    pq.push({max(H, heightMap[row][col]), row, col});
                }
            }
        }

        return ans;
    }
};
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