<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:
    struct comp {
        bool operator()(vector<int>& a, vector<int>& b) {
            return a[0] > b[0];
        }
    };

    int trapRainWater(vector<vector<int>>& heightMap) {
        
        if (heightMap.empty()) return 0;

        int N = heightMap.size();
        int M = heightMap[0].size();
        
        int ans = 0;
        int recH = 0;
        vector<int> mr = {-1, 1, 0, 0};
        vector<int> mc = {0, 0, -1, 1};
        vector<vector<bool>> visited(N, vector<bool>(M, false));
        priority_queue<vector<int>, vector<vector<int>>, comp> mQ;

        for (int i = 0; i < M; i++) {
            mQ.push({heightMap[0][i], 0, i});
            mQ.push({heightMap[N - 1][i], N - 1, i});
            visited[0][i] = true;
            visited[N - 1][i] = true;
        }

        for (int i = 1; i < N - 1; i++) {
            mQ.push({heightMap[i][0], i, 0});
            mQ.push({heightMap[i][M - 1], i, M - 1});
            visited[i][0] = true;
            visited[i][M - 1] = true;
        }

        while (!mQ.empty()) {
            vector<int> cur = mQ.top();
            mQ.pop();
            recH = max(recH, cur[0]);
            for (int i = 0; i < 4; i++) {
                int nr = cur[1] + mr[i];
                int nc = cur[2] + mc[i];
                if (nr >= 0 && nr < N && nc >= 0 && nc < M && (!visited[nr][nc])) {
                    ans += max(0, recH - heightMap[nr][nc]);
                    mQ.push({heightMap[nr][nc], nr, nc});
                    visited[nr][nc] = true;
                } 
            }
        }

        return ans;
    }
};
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