> 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/check-if-there-is-a-valid-path-in-a-grid.md).

# Check if There is a Valid Path in a Grid

 Given a *m* x *n* `grid`. Each cell of the `grid` represents a street. The street of `grid[i][j]` can be:

* **1** which means a street connecting the left cell and the right cell.
* **2** which means a street connecting the upper cell and the lower cell.
* **3** which means a street connecting the left cell and the lower cell.
* **4** which means a street connecting the right cell and the lower cell.
* **5** which means a street connecting the left cell and the upper cell.
* **6** which means a street connecting the right cell and the upper cell.

![](https://assets.leetcode.com/uploads/2020/03/05/main.png)

You will initially start at the street of the upper-left cell `(0,0)`. A valid path in the grid is a path which starts from the upper left cell `(0,0)` and ends at the bottom-right cell `(m - 1, n - 1)`. **The path should only follow the streets**.

**Notice** that you are **not allowed** to change any street.

Return true if there is a valid path in the grid or *false* otherwise.

**Example 1:**![](https://assets.leetcode.com/uploads/2020/03/05/e1.png)

```
Input: grid = [[2,4,3],[6,5,2]]
Output: true
Explanation: As shown you can start at cell (0, 0) and visit all the cells of the grid to reach (m - 1, n - 1).
```

**Example 2:**![](https://assets.leetcode.com/uploads/2020/03/05/e2.png)

```
Input: grid = [[1,2,1],[1,2,1]]
Output: false
Explanation: As shown you the street at cell (0, 0) is not connected with any street of any other cell and you will get stuck at cell (0, 0)
```

**Example 3:**

```
Input: grid = [[1,1,2]]
Output: false
Explanation: You will get stuck at cell (0, 1) and you cannot reach cell (0, 2).
```

**Example 4:**

```
Input: grid = [[1,1,1,1,1,1,3]]
Output: true
```

**Example 5:**

```
Input: grid = [[2],[2],[2],[2],[2],[2],[6]]
Output: true
```

**Constraints:**

* `m == grid.length`
* `n == grid[i].length`
* `1 <= m, n <= 300`
* `1 <= grid[i][j] <= 6`

```java
public class Solution {
    public boolean hasValidPath(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        return dfs(grid, m, n, 0, 0);
    }

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

    boolean dfs(int[][] grid, int m, int n, int r, int c) {
        if (r == m - 1 && c == n - 1)
            return true; // Reach bottom-right cell -> Valid path
        int value = grid[r][c];
        grid[r][c] = 0;
        for (int[] nextDir : DIR[value - 1]) {
            int nr = r + nextDir[0], nc = c + nextDir[1];
            if (nr < 0 || nr >= m || nc < 0 || nc >= n || grid[nr][nc] == 0)
                continue;
            for (int[] backDir : DIR[grid[nr][nc] - 1]) {
                // Check if next cell has a connected road
                if (nr + backDir[0] == r && nc + backDir[1] == c) {
                    if (dfs(grid, m, n, nr, nc))
                        return true;
                }
            }
        }
        grid[r][c] = value;
        return false;
    }
}
```