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Jump Game III

Given an array of non-negative integers arr, you are initially positioned at start index of the array.

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 any index with value 0.

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

Jump Game III diagram

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

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