1306-jump-game-iii.py

"""
Problem Link: https://leetcode.com/problems/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 * 104
0 <= arr[i] < arr.length
0 <= start < arr.length
"""
class Solution:
    def canReach(self, arr: List[int], start: int) -> bool:
        return self.helper(start, arr, set())
    
    def helper(self, index, arr, visited):
        if index < 0 or index >= len(arr) or index in visited:
            return False
        
        if arr[index] == 0:
            return True
        visited.add(index)
        
        return self.helper(index + arr[index], arr, visited) or self.helper(index - arr[index], arr, visited)