<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>

from collections import defaultdict
class Solution:
    
    def getAdjacencyMatrix(self, arr):
        matrix = defaultdict(list)
        end = []
        for idx, num in enumerate(arr):
            # print(idx, num)
            if num == 0:
                end.append(idx)
            
            if (idx - num) >= 0:
                matrix[idx].append(idx - num)
            if (idx + num) < len(arr):
                matrix[idx].append(num + idx)
        return matrix, end

    

    def canReach(self, arr: List[int], start: int) -> bool:



        matrix, endIdx = self.getAdjacencyMatrix(arr)
        # print(matrix)
        if start in endIdx:
            return True
        queue = [start]
        visited = [0]*len(arr)
        while queue:
            currNode = queue.pop(0)
            visited[currNode] = 1
            
            neighbours = matrix[currNode]
            # print(neighbours)
            for nb in neighbours:
                if nb in endIdx:
                    return True
                if not visited[nb]:
                    queue.append(nb)
        return False
        

        
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