<p>Given an array of non-negative integers <code>arr</code>, you are initially positioned at <code>start</code>&nbsp;index of the array. When you are at index <code>i</code>, you can jump&nbsp;to <code>i + arr[i]</code> or <code>i - arr[i]</code>, check if you can reach&nbsp;<strong>any</strong> index with value 0.</p>

<p>Notice that you can not jump outside of the array at any time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [4,2,3,0,3,1,2], start = 5
<strong>Output:</strong> true
<strong>Explanation:</strong> 
All possible ways to reach at index 3 with value 0 are: 
index 5 -&gt; index 4 -&gt; index 1 -&gt; index 3 
index 5 -&gt; index 6 -&gt; index 4 -&gt; index 1 -&gt; index 3 
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [4,2,3,0,3,1,2], start = 0
<strong>Output:</strong> true 
<strong>Explanation: 
</strong>One possible way to reach at index 3 with value 0 is: 
index 0 -&gt; index 4 -&gt; index 1 -&gt; index 3
</pre>

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= arr[i] &lt;&nbsp;arr.length</code></li>
	<li><code>0 &lt;= start &lt; arr.length</code></li>
</ul>

class Solution:
    def canReach(self, arr: List[int], start: int) -> bool:
        visited = set((start, ))

        def dfs(curr, visited):
            if not 0 <= curr < len(arr):
                return False
            if arr[curr] == 0:
                return True
            for next_idx in (curr + arr[curr], curr - arr[curr]):
                if next_idx not in visited:
                    visited.add(next_idx)
                    if dfs(next_idx, visited):
                        return True
            return False

        return dfs(start, visited)



    ''' BFS '''
    # def canReach(self, arr: List[int], start: int) -> bool:
    #     visited = set((start, ))
    #     queue = deque([start])
    #     while queue:
    #         curr = queue.popleft()
    #         if arr[curr] == 0:
    #             return True
    #         if 0 <= curr + arr[curr] < len(arr) and curr + arr[curr] not in visited:
    #             queue.append(curr + arr[curr])
    #             visited.add(curr + arr[curr])
    #         if 0 <= curr - arr[curr] < len(arr) and curr - arr[curr] not in visited:
    #             queue.append(curr - arr[curr])
    #             visited.add(curr - arr[curr])
    #     return False

35300