<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>

#include <vector>
#include <queue>
#include <algorithm>

class Solution {
public:
  int trapRainWater(std::vector<std::vector<int>>& heightMap) {
    if (heightMap.empty() || heightMap[0].empty()) return 0;
    
    int m = heightMap.size();
    int n = heightMap[0].size();
    
    // Min-heap to store the boundary cells, sorted by their height
    std::priority_queue<std::pair<int, std::pair<int, int>>, 
                        std::vector<std::pair<int, std::pair<int, int>>>, 
                        std::greater<std::pair<int, std::pair<int, int>>>> minHeap;
    
    // Visited matrix to keep track of visited cells
    std::vector<std::vector<bool>> visited(m, std::vector<bool>(n, false));
    
    // Add all boundary cells to the heap
    for (int i = 0; i < m; i++) {
      for (int j = 0; j < n; j++) {
        if (i == 0 || i == m - 1 || j == 0 || j == n - 1) {
          minHeap.push({heightMap[i][j], {i, j}});
          visited[i][j] = true; // Mark boundary cells as visited
        }
      }
    }
    
    int waterTrapped = 0;
    std::vector<std::vector<int>> directions = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    
    // Process cells from the min-heap
    while (!minHeap.empty()) {
      auto cell = minHeap.top();
      minHeap.pop();
      
      int height = cell.first;
      int x = cell.second.first;
      int y = cell.second.second;
      
      // Explore all 4 possible directions
      for (auto dir : directions) {
        int nx = x + dir[0];
        int ny = y + dir[1];
        
        if (nx >= 0 && nx < m && ny >= 0 && ny < n && !visited[nx][ny]) {
          visited[nx][ny] = true;
          waterTrapped += std::max(0, height - heightMap[nx][ny]);
          minHeap.push({std::max(heightMap[nx][ny], height), {nx, ny}});
        }
      }
    }
    
    return waterTrapped;
  }
};

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