> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/priority-queue/trapping-rain-water-ii.md).

# Trapping Rain Water II

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.

**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.
```

![](https://assets.leetcode.com/uploads/2018/10/13/rainwater_empty.png)

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.

![](https://assets.leetcode.com/uploads/2018/10/13/rainwater_fill.png)

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

**Constraints:**

* `1 <= m, n <= 110`
* `0 <= heightMap[i][j] <= 20000`

```java
class Solution {
    // https://drive.google.com/file/d/1YHHlkHkx5Ae9Ft9dAHMV52HMnOCnYcMF/view?usp=sharing
    static class Pair {
        int x, y, val;

        Pair(int x, int y, int v) {
            this.x = x;
            this.y = y;
            this.val = v;
        }
    }

    public int trapRainWater(int[][] heightMap) {
        int m = heightMap.length, n = heightMap[0].length;
        if (m == 1 || n == 1)
            return 0;
        // Priority Queue hold virtual border which holds water inside
        // Therefore starting border is border of matrix
        PriorityQueue<Pair> pq = new PriorityQueue<>((a, b) -> a.val - b.val);
        boolean[][] visited = new boolean[m][n];
        for (int i = 0; i < m; i++) {
            pq.add(new Pair(i, 0, heightMap[i][0]));
            visited[i][0] = true;
            pq.add(new Pair(i, n - 1, heightMap[i][n - 1]));
            visited[i][n - 1] = true;
        }
        for (int i = 1; i < n - 1; i++) {
            pq.add(new Pair(0, i, heightMap[0][i]));
            visited[0][i] = true;
            pq.add(new Pair(m - 1, i, heightMap[m - 1][i]));
            visited[m - 1][i] = true;
        }
        // Now we want to find smallest height, and check all unvisited neighbors
        // If any neighbor < border height(min), then we can add this water to our
        // answer, as it cannot flow out of border from any direction
        int[][] dirs = { { 1, 0 }, { 0, 1 }, { -1, 0 }, { 0, -1 } };
        int ans = 0;
        while (pq.size() != 0) {
            Pair smallest = pq.poll();
            int x = smallest.x, y = smallest.y;
            for (int[] dir : dirs) {
                int newX = x + dir[0], newY = y + dir[1];
                if (newX >= 0 && newX < m && newY >= 0 && newY < n && !visited[newX][newY]) {
                    visited[newX][newY] = true;
                    // If we can store some water here, then this stored water
                    // will also work as a wall in our virtual border
                    if (heightMap[newX][newY] < smallest.val) {
                        ans += smallest.val - heightMap[newX][newY];
                        pq.add(new Pair(newX, newY, smallest.val));
                    } else
                        pq.add(new Pair(newX, newY, heightMap[newX][newY]));
                }
            }
        }
        return ans;
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/priority-queue/trapping-rain-water-ii.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.