<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:
    def trapRainWater(self, heightMap: List[List[int]]) -> int:
        if not heightMap or not heightMap[0]:
            return 0
        
        ROWS, COLS = len(heightMap), len(heightMap[0])

        if ROWS < 3 or COLS < 3:
            return 0
        
        heap = []
        visit = set()

        for c in range(COLS):
            heapq.heappush(heap, (heightMap[0][c], 0, c))
            heapq.heappush(heap, (heightMap[ROWS - 1][c], ROWS - 1, c))
            visit.add((0, c))
            visit.add((ROWS - 1, c)) 
        for r in range(ROWS):
            heapq.heappush(heap, (heightMap[r][0], r, 0))
            heapq.heappush(heap, (heightMap[r][COLS - 1], r, COLS - 1))
            visit.add((r, COLS - 1))
            visit.add((r, 0))
            
       
        level, res = 0, 0

        while heap:
            height, r, c = heapq.heappop(heap)
            level = max(height, level)

            neigh = [[0, 1], [0, -1], [1, 0], [-1, 0]]

            for dr, dc in neigh:
                if (dr + r) < 0 or (c + dc) < 0 or (dr + r) >= ROWS or (c + dc) >= COLS or (dr + r, dc + c) in visit:
                    continue
            
                heapq.heappush(heap, (heightMap[dr + r][dc + c], dr + r, dc + c))
                visit.add((dr + r, dc + c))
                if heightMap[dr + r][dc + c] < level:
                    res += level - heightMap[dr + r][dc + c]
        
        return res
                







        


23400