> 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/graphs-bfs-and-dfs/pacific-atlantic-water-flow.md).

# Pacific Atlantic Water Flow

Given an `m x n` matrix of non-negative integers representing the height of each unit cell in a continent, the "Pacific ocean" touches the left and top edges of the matrix and the "Atlantic ocean" touches the right and bottom edges.

Water can only flow in four directions (up, down, left, or right) from a cell to another one with height equal or lower.

Find the list of grid coordinates where water can flow to both the Pacific and Atlantic ocean.

**Note:**

1. The order of returned grid coordinates does not matter.
2. Both m and n are less than 150.

**Example:**

```
Given the following 5x5 matrix:

  Pacific ~   ~   ~   ~   ~ 
       ~  1   2   2   3  (5) *
       ~  3   2   3  (4) (4) *
       ~  2   4  (5)  3   1  *
       ~ (6) (7)  1   4   5  *
       ~ (5)  1   1   2   4  *
          *   *   *   *   * Atlantic

Return:

[[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]] (positions with parentheses in above matrix).
```

```java
public class Solution {
    // Use 2 visited matrices
    // Now in our dfs we are only marking visited
    // if the current height >= previous height
    public List<List<Integer>> pacificAtlantic(int[][] matrix) {
        List<List<Integer>> res = new LinkedList<>();
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return res;
        }
        int n = matrix.length, m = matrix[0].length;
        boolean[][] pacific = new boolean[n][m];
        boolean[][] atlantic = new boolean[n][m];
        for (int i = 0; i < n; i++) {
            dfs(matrix, pacific, Integer.MIN_VALUE, i, 0);
            dfs(matrix, atlantic, Integer.MIN_VALUE, i, m - 1);
        }
        for (int i = 0; i < m; i++) {
            dfs(matrix, pacific, Integer.MIN_VALUE, 0, i);
            dfs(matrix, atlantic, Integer.MIN_VALUE, n - 1, i);
        }
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                if (pacific[i][j] && atlantic[i][j]) {
                    List<Integer> point = new ArrayList<>();
                    point.add(i);
                    point.add(j);
                    res.add(point);
                }
        return res;
    }

    int[][] dir = new int[][] { { 0, 1 }, { 0, -1 }, { 1, 0 }, { -1, 0 } };

    public void dfs(int[][] matrix, boolean[][] visited, int height, int x, int y) {
        int n = matrix.length, m = matrix[0].length;
        if (x < 0 || x >= n || y < 0 || y >= m || visited[x][y] || matrix[x][y] < height)
            return;
        visited[x][y] = true;
        for (int[] d : dir)
            dfs(matrix, visited, matrix[x][y], x + d[0], y + d[1]);
    }
}
```


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