Given an m x n matrix of positive integers representing the height of each unit cell in a 2D elevation map, compute the volume of water it is able to trap after raining.

Note:

Both m and n are less than 110. The height of each unit cell is greater than 0 and is less than 20,000.

Example:

Given the following 3x6 height map:
[
  [1,4,3,1,3,2],
  [3,2,1,3,2,4],
  [2,3,3,2,3,1]
]

Return 4.

The above image represents the elevation map [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]] before the rain.

After the rain, water is trapped between the blocks. The total volume of water trapped is 4.

給定一個 m x n 的矩陣，其中的值均為正整數，代表二維高度圖每個單元的高度，請計算圖中形狀最多能接多少體積的雨水。

說明:

m 和 n 都是小於110的整數。每一個單位的高度都大於0 且小於 20000。

示例：

給出如下 3x6 的高度圖:
[
  [1,4,3,1,3,2],
  [3,2,1,3,2,4],
  [2,3,3,2,3,1]
]

返回 4。

如上圖所示，這是下雨前的高度圖[[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]] 的狀態。

下雨後，雨水將會被存儲在這些方塊中。總的接雨水量是4。

超出時間限制

 1 class Solution {
 2     func trapRainWater(_ heightMap: [[Int]]) -> Int {
 3         if heightMap.isEmpty {return
 
 0}
 4         var m:Int = heightMap.count
 5         var n:Int = heightMap[0].count
 6         var res:Int = 0
 7         var mx:Int = Int.min
 8         var q:[[Int]] = [[Int]]()
 9         var visited:[[Bool]] = [[Bool]](repeating:[Bool](repeating:false,count:n),count:m)
10         var dir:[[Int]] = [[0,-1],[-1,0],[0,1],[1,0]]
11         for i in 0..<m
12         {
13             for j in 0..<n
14             {
15                 if i == 0 || i == m - 1 || j == 0 || j == n - 1
16                 {
17                     q.append([heightMap[i][j], i * n + j])
18                     visited[i][j] = true
19                 }
20             }
21         }
22         while(!q.isEmpty)
23         {
24             q = q.sorted { $0[0] == $1[0] ? $0[1] < $1[1] : $0[0] > $1[0] }
25             var t:[Int] = q.removeLast()           
26             var h:Int = t[0]
27             var r:Int = t[1] / n
28             var c:Int = t[1] % n
29             mx = max(mx, h)
30             for i in 0..<dir.count
31             {
32                 var x:Int = r + dir[i][0]
33                 var y:Int = c + dir[i][1]
34                 if x < 0 || x >= m || y < 0 || y >= n || visited[x][y]
35                 {
36                     continue
37                 }
38                 visited[x][y] = true
39                 if heightMap[x][y] < mx
40                 {
41                     res += mx - heightMap[x][y]
42                 }
43                 q.append([heightMap[x][y], x * n + y])
44             }
45         }
46         return res
47     }
48 }

[Swift]LeetCode407. 接雨水 II | Trapping Rain Water II