<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 Node {
public:
    int i, j, h;
    Node(int a, int b, int c) : i(a), j(b), h(c) {}
    bool operator>(const Node& b) const { return h > b.h; }
    bool operator<(const Node& b) const { return h < b.h; }
};

class Solution {
public:
    vector<vector<int>> dirs{{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
    int m, n;

    const bool check(int i, int j){
        return 0 <= i && i < m && 0 <= j && j < n;
    }

    int trapRainWater(vector<vector<int>>& heights) {
        m = heights.size(), n = heights[0].size();
        priority_queue<Node, vector<Node>, greater<Node>> heap;
        for (int i = 0; i < m; i++){
            heap.push(Node(i, 0, heights[i][0]));
            heap.push(Node(i, n - 1, heights[i][n - 1]));
            heights[i][0] = heights[i][n - 1] = -1;
        }
        for (int j = 1; j < n - 1; j++){
            heap.push(Node(0, j, heights[0][j]));
            heap.push(Node(m - 1, j, heights[m - 1][j]));
            heights[0][j] = heights[m - 1][j] = -1;
        }
        int res = 0;
        while (!heap.empty()){
            Node top = heap.top();
            heap.pop();
            for (auto dir : dirs){
                int i = top.i + dir[0], j = top.j + dir[1];
                if (check(i, j) && heights[i][j] >= 0){
                    if (heights[i][j] >= top.h){
                        heap.push(Node(i, j, heights[i][j]));
                    } else {
                        heap.push(Node(i, j, top.h));
                        res += top.h - heights[i][j];
                    }
                    heights[i][j] = -1;
                }
            }
        }
        return res;
    }
};
37631