# 1306. 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.

# Solution

Approach 1: search (BFS or DFS).

# Code (Python)

Approach 1:

    def canReach(self, arr: List[int], start: int) -> bool:
        stack = [start]
        visited = set([start])
        while stack:
            position = stack.pop()
            if arr[position] == 0:
                return True
            for new_pos in (position + arr[position], position - arr[position]):
                if 0 <= new_pos < len(arr) and new_pos not in visited:
                    stack.append(new_pos)
                    visited.add(new_pos)
        return False

# Code (C++)

Approach 1:

Approach 2: