<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 MatrixPoint {
        int height;
        int row;
        int col;
        MatrixPoint(int h, int r, int c): height(h), row(r), col(c) {}
    };

    struct customLess {
        bool operator()(const MatrixPoint* l, const MatrixPoint* r) const { return l->height > r->height; }
    };

    int trapRainWater(vector<vector<int>>& heightMap) {
        if (heightMap.size() <= 2 || heightMap[0].size() <= 2) return 0;
        int m = heightMap.size(), n = heightMap[0].size();
        priority_queue<MatrixPoint*, vector<MatrixPoint*>, customLess> pq;
        vector<vector<int>> visited(m, vector<int>(n, 0));
        for (int i = 0; i < m; ++i) {
            pq.push(new MatrixPoint(heightMap[i][0], i, 0));
            pq.push(new MatrixPoint(heightMap[i][n-1], i, n-1));
            visited[i][0] = visited[i][n-1] = 1;
        }
        for (int i = 0; i < n; ++i) {
            pq.push(new MatrixPoint(heightMap[0][i], 0, i));
            pq.push(new MatrixPoint(heightMap[m-1][i], m-1, i));
            visited[0][i] = visited[m-1][i] = 1;
        }

        int directions[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
        int sum = 0;
        while (!pq.empty()) {
            auto point = pq.top();
            pq.pop();

            int height = point->height, row = point->row, col = point->col;
            for (int i = 0; i < 4; ++i) {
                int cur_row = row + directions[i][0], cur_col = col + directions[i][1];
                if (cur_row < 0 || cur_row >= m || cur_col < 0 || cur_col >= n || visited[cur_row][cur_col]) {
                    continue;
                }
                if (heightMap[cur_row][cur_col] < height) {
                    sum += height - heightMap[cur_row][cur_col];
                }
                visited[cur_row][cur_col] = 1;
                pq.push(new MatrixPoint(max(heightMap[cur_row][cur_col], height), cur_row, cur_col));
            }
        }
        return sum;
    }
};

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