# Trapping Rain Water II Problem

## Description

LeetCode Problem 407.

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:

``````1
2
3
4
5
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:

``````1
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 * 10^4

## Sample C++ Code

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
class Solution {
public:
int trapRainWater(vector<vector<int>>& heightMap) {
int m = heightMap.size(), n = (m == 0) ? 0 : heightMap[0].size();
if (m < 3 || n < 3) return 0;
priority_queue<pair<int, pair<int, int>>, vector<pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> pq;
vector<vector<int>> visited(m, vector<int>(n, 0));
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (!(i == 0 || i == m-1 || j == 0 || j == n-1)) continue;
pq.push(make_pair(heightMap[i][j], make_pair(i, j)));
visited[i][j] = 1;
}
}
vector<int> dir = {0, 1, 0, -1, 0};
int H = INT_MIN;
int res = 0;
while (!pq.empty()) {
auto p = pq.top(); pq.pop();
int height = p.first, i = p.second.first, j = p.second.second;
H = max(H, height);
for (int d = 0; d < 4; d++) {
int x = i + dir[d], y = j + dir[d+1];
if (x < 0 || x >= m || y < 0 || y >= n || visited[x][y]) continue;
visited[x][y] = 1;
int diff = H - heightMap[x][y];
if (diff > 0) res += diff;
pq.push(make_pair(heightMap[x][y], make_pair(x, y)));
}
}
return res;
}
};
``````