<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>

struct T {
  int i;
  int j;
  int h;  // heightMap[i][j] or the height after filling water
};

class Solution {
 public:
  int trapRainWater(vector<vector<int>>& heightMap) {
    constexpr int dirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    const int m = heightMap.size();
    const int n = heightMap[0].size();
    int ans = 0;
    auto compare = [](const T& a, const T& b) { return a.h > b.h; };
    priority_queue<T, vector<T>, decltype(compare)> minHeap(compare);
    vector<vector<bool>> seen(m, vector<bool>(n));

    for (int i = 0; i < m; ++i) {
      minHeap.emplace(i, 0, heightMap[i][0]);
      minHeap.emplace(i, n - 1, heightMap[i][n - 1]);
      seen[i][0] = true;
      seen[i][n - 1] = true;
    }

    for (int j = 1; j < n - 1; ++j) {
      minHeap.emplace(0, j, heightMap[0][j]);
      minHeap.emplace(m - 1, j, heightMap[m - 1][j]);
      seen[0][j] = true;
      seen[m - 1][j] = true;
    }

    while (!minHeap.empty()) {
      const auto [i, j, h] = minHeap.top();
      minHeap.pop();
      for (const auto& [dx, dy] : dirs) {
        const int x = i + dx;
        const int y = j + dy;
        if (x < 0 || x == m || y < 0 || y == n)
          continue;
        if (seen[x][y])
          continue;
        if (heightMap[x][y] < h) {
          ans += h - heightMap[x][y];
          minHeap.emplace(x, y, h);  // Fill water in grid[x][y].
        } else {
          minHeap.emplace(x, y, heightMap[x][y]);
        }
        seen[x][y] = true;
      }
    }

    return ans;
  }
};
18256