# 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: