<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();

        // Min-heap to store boundary cells
        priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<>> heap;

        // Mark boundary cells and add to heap
        for (int i = 0; i < m; ++i) {
            heap.push({heightMap[i][0], i, 0});
            heap.push({heightMap[i][n-1], i, n-1});

            heightMap[i][0] = -1; // Mark as visited
            heightMap[i][n-1] = -1;
        }

        for (int j = 1; j < n-1; ++j) {
            heap.push({heightMap[0][j], 0, j});
            heap.push({heightMap[m-1][j], m-1, j});

            heightMap[0][j] = -1;
            heightMap[m-1][j] = -1;
        }

        int level = 0, res = 0;
        vector<pair<int, int>> directions = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};

        // Process the heap
        while (!heap.empty()) {
            auto [height, x, y] = heap.top();
            heap.pop();
            level = max(height, level);

            // Explore neighboring cells
            for (const auto& [dx, dy] : directions) {
                int i = x + dx;
                int j = y + dy;
                if (i >= 0 && i < m && j >= 0 && j < n && heightMap[i][j] != -1) {
                    heap.push({heightMap[i][j], i, j});
                    if (heightMap[i][j] < level) {
                        res += level - heightMap[i][j];
                    }
                    heightMap[i][j] = -1; // Mark as visited
                }
            }
        }

        return res;
    }
};
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