<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>>>
            q;
        array<pair<int, int>, 4> dirs = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
        int trapped = 0;
        int n = heightMap.size();
        int m = heightMap[0].size();
        for (int i = 0; i < n; i++) {
            q.push({heightMap[i][0], i, 0});
            heightMap[i][0] = -1;
            q.push({heightMap[i][m - 1], i, m - 1});
            heightMap[i][m - 1] = -1;
        }
        for (int i = 0; i < m; i++) {
            q.push({heightMap[0][i], 0, i});
            heightMap[0][i] = -1;
            q.push({heightMap[n - 1][i], n - 1, i});
            heightMap[n - 1][i] = -1;
        }
        int level = 0;
        while (!q.empty()) {
            auto el = q.top();
            q.pop();
            int h = el[0];
            int r = el[1];
            int c = el[2];

            level = max(h, level);

            for (auto [dr, dc] : dirs) {
                int r1 = r + dr;
                int c1 = c + dc;
                if (r1 >= 0 && c1 >= 0 && r1 < n && c1 < m && heightMap[r1][c1] != -1) {
                    if (heightMap[r1][c1] < level)
                        trapped += (level - heightMap[r1][c1]);
                    q.push({heightMap[r1][c1], r1, c1});
                    heightMap[r1][c1] = -1;
                }
            }
        }
        return trapped;
    }
};
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