> 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/dynamic-programming/jump-game-iii.md).

# Jump Game III

Given an array of non-negative integers `arr`, you are initially positioned at `start` index of the array. When you are at index `i`, you can jump to `i + arr[i]` or `i - arr[i]`, check if you can reach to **any** index with value 0.

Notice that you can not jump outside of the array at any time.

**Example 1:**

```
Input: arr = [4,2,3,0,3,1,2], start = 5
Output: true
Explanation: 
All possible ways to reach at index 3 with value 0 are: 
index 5 -> index 4 -> index 1 -> index 3 
index 5 -> index 6 -> index 4 -> index 1 -> index 3 
```

**Example 2:**

```
Input: arr = [4,2,3,0,3,1,2], start = 0
Output: true 
Explanation: 
One possible way to reach at index 3 with value 0 is: 
index 0 -> index 4 -> index 1 -> index 3
```

**Example 3:**

```
Input: arr = [3,0,2,1,2], start = 2
Output: false
Explanation: There is no way to reach at index 1 with value 0.
```

**Constraints:**

* `1 <= arr.length <= 5 * 10^4`
* `0 <= arr[i] < arr.length`
* `0 <= start < arr.length`

```java
class Solution {
    public boolean backtrack(int[] arr, int start, boolean[] visited) {
        if (start < 0 || start >= visited.length || visited[start])
            return false;
        if (arr[start] == 0)
            return true;
        visited[start] = true;
        boolean ans = backtrack(arr, start + arr[start], visited) || backtrack(arr, start - arr[start], visited);
        visited[start] = false;
        return ans;
    }

    public boolean canReach(int[] arr, int start) {
        boolean[] visited = new boolean[arr.length];
        return backtrack(arr, start, visited);
    }
}
```