<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 <queue>
#include <set>
#include <tuple>
#include <vector>

class Solution {
 public:
  int trapRainWater(std::vector<std::vector<int>>& heightMap) {
    struct Cell {
      int x;
      int y;
      int height;
    };

    auto cmp = [](const Cell& l, const Cell& r) { return l.height > r.height; };

    // min heap
    std::priority_queue<Cell, std::vector<Cell>, decltype(cmp)> q(cmp);
    std::set<std::pair<int, int>> visited;

    auto mark = [&](int x, int y, int height = 0) {
      q.emplace(x, y, std::max(heightMap[x][y], height));
      visited.emplace(x, y);
    };

    // init
    // 1 <= m, n <= 200
    const int m = heightMap.size();
    const int n = heightMap[0].size();
    for (int i = 0; i < m; i++) {
      mark(i, 0);
      mark(i, n - 1);
    }

    for (int j = 0; j < n; j++) {
      mark(0, j);
      mark(m - 1, j);
    }

    // algorithm
    int clockwise[] = {-1, 0, 1, 0, -1};
    int totalTrapped = 0;

    while (!q.empty()) {
      auto [x, y, baseHeight] = q.top();
      q.pop();

      for (int i = 0; i < 4; i++) {
        int nx = x + clockwise[i];
        int ny = y + clockwise[i + 1];
        if (nx >= 0 && nx < m && ny >= 0 && ny < n && !visited.contains({nx, ny})) {
          int height = heightMap[nx][ny];
          if (baseHeight > height) {
            totalTrapped += (baseHeight - height);
          }

          mark(nx, ny, baseHeight);
        }
      }
    }
    return totalTrapped;
  }
};
27006