<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)
    {
        priority_queue<pair<int, pair<int, int>>, vector<pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> pq;
        int n = heightMap.size();
        if (n == 0)
        {
            return 0;
        }
        int m = heightMap[0].size();
        vector<vector<int>> vis(n, vector<int>(m, 0));
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                if (i == 0 || j == 0 || i == n - 1 || j == m - 1)
                {
                    vis[i][j] = 1;
                    pq.push({heightMap[i][j], {i, j}});
                }
            }
        }
        int ans = 0;
        vector<pair<int, int>> d = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
        while (!pq.empty())
        {
            auto x = pq.top();
            pq.pop();
            int height = x.first;
            int i = x.second.first;
            int j = x.second.second;
            cout<<i<<" "<<j<<"\n";
            for (auto dir : d)
            {
                int d_i = i + dir.first;
                int d_j = j + dir.second;
                if (d_i >= 0 && d_j >= 0 && d_i < n && d_j < m && !vis[d_i][d_j])
                {
                    int n_height = heightMap[d_i][d_j];
                    if (n_height >= height)
                    {
                        pq.push({n_height, {d_i, d_j}});
                    }else{
                        ans += height - n_height;
                        pq.push({height, {d_i, d_j}});
                    }
                    vis[d_i][d_j] = 1;
                }
            }
        }
        return ans;
    }
};
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