<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:
        from queue import PriorityQueue

        if len(heightMap) == 0:
            return 0
        elif len(heightMap[0]) == 0:
            return 0
        n, m = len(heightMap), len(heightMap[0])
        if n==1 and m==1:
            return 0
        
        q = PriorityQueue()
        visited = set()
        directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]
        escape = [[0] * m for i in range(n)]

        for i in range(n-1):
            q.put((heightMap[i][0], (i, 0)))
            escape[i][0] = heightMap[i][0]
            visited.add((i, 0))
            q.put((heightMap[i+1][m-1], (i+1, m-1)))
            escape[i+1][m-1] = heightMap[i+1][m-1]
            visited.add((i+1, m-1))
        for j in range(m-1):
            q.put((heightMap[0][j+1], (0, j+1)))
            escape[0][j+1] = heightMap[0][j+1]
            visited.add((0, j+1))
            q.put((heightMap[n-1][j], (n-1, j)))
            escape[n-1][j] = heightMap[n-1][j]
            visited.add((n-1, j))
        
        while not q.empty():
            v, (i, j) = q.get()
            # print(v, i, j)
            for di, dj in directions:
                ni, nj = i+di, j+dj
                if (ni >= 0) and (ni < n) and (nj >= 0) and (nj < m):
                    if (ni, nj) not in visited:
                        q.put((max(v, heightMap[ni][nj]), (ni, nj)))
                        visited.add((ni, nj))
                        escape[ni][nj] = max(v, heightMap[ni][nj])
                        # if v >= heightMap[ni][nj]:
                        #     visited.add((ni, nj))
                        #     q.put((v, (ni, nj)))
                        #     print('-', v, ni, nj)
                        #     escape[ni][nj] = v
                        # elif (escape[ni][nj]== 0) or (v <= escape[ni][nj]):
                        #     escape[ni][nj] = v
                        #     visited.add((ni, nj))
            # for row in escape:
            #     print(row)
        
        ans = 0

        # print(escape)

        for i in range(n):
            for j in range(m):
                if escape[i][j] > heightMap[i][j]:
                    ans += escape[i][j] - heightMap[i][j]

        return ans


        

        


        l = [([0] * n) for _ in range(m)]
        r = [([0] * n) for _ in range(m)]
        u = [([0] * n) for _ in range(m)]
        d = [([0] * n) for _ in range(m)]
        for i in range(m):
            l[i][0] = heightMap[i][0]
            r[i][n-1] = heightMap[i][n-1]
            for j in range(1, n):
                l[i][j] = max(l[i][j-1], heightMap[i][j])
                r[i][n-j-1] = max(r[i][n-j], heightMap[i][n-j-1])
        for j in range(n):
            u[0][j] = heightMap[0][j]
            d[m-1][j] = heightMap[m-1][j]
            for i in range(1, m):
                u[i][j] = max(u[i-1][j], heightMap[i][j])
                d[m-i-1][j] = max(d[m-i][j], heightMap[m-i-1][j])
                
        print(l)
        print(r)
        print(u)
        print(d)
                
        ans = 0
        for i in range(m):
            for j in range(n):
                # print(heightMap[i][j], min(l[i][j], r[i][j], u[i][j], d[i][j]))
                ans += min(l[i][j], r[i][j], u[i][j], d[i][j]) - heightMap[i][j]
                
        return ans
23100