<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) {
        int m = heightMap.size(), n = heightMap[0].size(), ans = 0;
        priority_queue<pair<int, pair<int, int>>, vector<pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> q;
        set<pair<int, int>> visit;
        int dir[][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
        for(int i = 0; i < m; i++){
            q.push({heightMap[i][0], {i, 0}});
            visit.insert({i, 0});
            q.push({heightMap[i][n-1], {i, n-1}});
            visit.insert({i, n-1});
        }
        for(int j = 1; j < n-1; j++){
            q.push({heightMap[0][j], {0, j}});
            visit.insert({0, j});
            q.push({heightMap[m-1][j], {m-1, j}});
            visit.insert({m-1, j});
        }
        while(!q.empty()){
            int h = q.top().first, i = q.top().second.first, j = q.top().second.second;
            q.pop();

            for(int k = 0; k < 4; k++){
                int x = i + dir[k][0], y = j + dir[k][1];
                if(x < 0 || x >= m || y < 0 || y >= n || visit.find({x,y}) != visit.end())
                    continue;
                if(heightMap[x][y] < h){
                    ans += h-heightMap[x][y];
                    visit.insert({x, y});
                    q.push({h, {x,y}});
                }
                else{
                    visit.insert({x, y});
                    q.push({heightMap[x][y], {x,y}});
                }
            }
        }
        return ans;
    }
};
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