<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) {
        if (heightMap.empty() || heightMap[0].empty()) {
            return 0;
        }
        int m = heightMap.size();
        int n = heightMap[0].size();
        vector<vector<bool>> visited(m, vector<bool>(n, false));
        vector<vector<int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
        auto comparator = [&](const pair<int, vector<int>>& a, const pair<int, vector<int>>& b) {return a.first  >= b.first;};
        priority_queue<pair<int, vector<int>>, vector<pair<int, vector<int>>>, decltype(comparator)> pq(comparator);
        for (int i = 0; i < m; ++i) {
            pq.push({heightMap[i][0], {i, 0}});
            pq.push({heightMap[i][n - 1], {i, n - 1}});
            visited[i][0] = true;
            visited[i][n - 1] = true;
        }
        for (int j = 0; j < n; ++j) {
            pq.push({heightMap[0][j], {0, j}});
            pq.push({heightMap[m - 1][j], {m - 1, j}});
            visited[0][j] = true;
            visited[m - 1][j] = true;
        }
        int res = 0;
        while (!pq.empty()) {
            auto [h, vec] = pq.top();
            int i = vec[0];
            int j = vec[1];
            pq.pop();
            for (auto& d: directions) {
                int ii = i + d[0];
                int jj = j + d[1];
                if (ii < 0 || ii >= m || jj < 0 || jj >= n || visited[ii][jj]) {
                    continue;
                }
                visited[ii][jj] = true;
                if (heightMap[ii][jj] < h) {
                    res += h - heightMap[ii][jj];
                }
                pq.push({max(h, heightMap[ii][jj]), {ii, jj}});
            }
            
        }
        return res;
    }
};
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