<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 cmp {
    bool operator()(const vector<int>& a, const vector<int>& b) {
        return a[0]>b[0];
    }

};

class Solution {
private:
    int m, n;
    int ans;
    priority_queue<vector<int>, vector<vector<int>>, cmp> min_heap;
    vector<vector<bool>> visited;
public:
    int trapRainWater(vector<vector<int>>& heightMap) {
        ans = 0;
        m = heightMap.size();
        n = heightMap[0].size();
        visited.resize(m, vector<bool>(n, false));
        

        // for(int i=0; i<m; i++) {
        //     for(int j=0; j<n; j++) {
        //         // area -= (heightMap[i][j] == -1);
        //         printf("%d ", heightMap[i][j]);
        //     }
        //     printf("\n");
        // }
        for(int i=0; i<m; i++) {
            min_heap.push({heightMap[i][0], i, 0});
            min_heap.push({heightMap[i][n-1], i, n-1});
            visited[i][0] = true;
            visited[i][n-1] = true;
        }
        for(int j=1; j<n-1; j++) {
            min_heap.push({heightMap[0][j], 0, j});
            min_heap.push({heightMap[m-1][j], m-1, j});
            visited[0][j] = true;
            visited[m-1][j] = true;
            // dfs(heightMap, 0, j, heightMap[0][j]);
            // dfs(heightMap, m-1, j, heightMap[m-1][j]);
        }

        int area = 0;
        int dirs[5] = {0, 1, 0, -1, 0};
        while(!min_heap.empty()) {
            vector<int> edge = min_heap.top(); min_heap.pop();
            for(int d=0; d<4; d++) {
                int i = edge[1]+dirs[d];
                int j = edge[2]+dirs[d+1];
                if(i<0 || j<0 || i==m || j==n || visited[i][j]) continue;
                if(edge[0] > heightMap[i][j]) ans+= edge[0] - heightMap[i][j];
                visited[i][j] = true;
                min_heap.push({max(edge[0], heightMap[i][j]), i, j});
            }

            // printf("thres:%d i:%d j:%d\n", edge[0], i, j);
            // dfs(heightMap, i, j, edge[0]);
        }
        return ans;
        
    }

};
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