Difficulty: Hard
Tags: LeetCode, Hard, Breadth-First Search, Array, Matrix, Heap (Priority Queue), leetcode-407, Binary Heap, O(m * n * (logm + logn)), O(m * n), LintCode, Heap, BFS, Tricky

Problem

Given an m x n integer matrix heightMap representing the height of each unit cell in a 2D elevation map, return the volume of water it can trap after raining.

Example 1:

Input: heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]
Output: 4
Explanation: 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.

Example 2:

Input: 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]]
Output: 10

Constraints:

m == heightMap.length
n == heightMap[i].length
1 <= m, n <= 200
0 <= heightMap[i][j] <= 2 * 10⁴