<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>

static const auto f = []() {
    std::ios_base::sync_with_stdio(0);
    cin.tie(0);

    return 0;
}();

class Solution 
{
public:

    int trapRainWater(vector<vector<int>>& heightMap)
    {

        typedef pair<int, int> cell;
        priority_queue<cell, vector<cell>, greater<cell>> q;

        const int m = heightMap.size();

        if (m == 0) return 0;

        const int n = heightMap[0].size();

        vector<int> visited(m * n, false);

        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)
                {
                    if (!visited[i * n + j])
                        q.emplace(cell(heightMap[i][j], i * n + j));
                    visited[i * n + j] = true;
                }
            }
        }

        int dir[4][2] = { {0,1}, {0, -1}, {1, 0}, {-1, 0} };
        int ans = 0;

        while (!q.empty())
        {
            const cell curr_cell = q.top();
            q.pop();

            const int i = curr_cell.second / n, j = curr_cell.second % n;

            for (int r = 0; r < 4; ++r)
            {
                const int ii = i + dir[r][0], jj = j + dir[r][1];
                if (ii < 0 || ii >= m || jj < 0 || jj >= n || visited[ii * n + jj])
                    continue;

                ans += max(0, curr_cell.first - heightMap[ii][jj]);

                q.emplace(cell(max(curr_cell.first, heightMap[ii][jj]), ii * n + jj));
                visited[ii * n + jj] = true;
            }
        }

        return ans;
    }
};
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