<p>You are given the <code>root</code> of a binary tree with <strong>unique</strong> values, and an integer <code>start</code>. At minute <code>0</code>, an <strong>infection</strong> starts from the node with value <code>start</code>.</p>

<p>Each minute, a node becomes infected if:</p>

<ul>
	<li>The node is currently uninfected.</li>
	<li>The node is adjacent to an infected node.</li>
</ul>

<p>Return <em>the number of minutes needed for the entire tree to be infected.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/25/image-20220625231744-1.png" style="width: 400px; height: 306px;" />
<pre>
<strong>Input:</strong> root = [1,5,3,null,4,10,6,9,2], start = 3
<strong>Output:</strong> 4
<strong>Explanation:</strong> The following nodes are infected during:
- Minute 0: Node 3
- Minute 1: Nodes 1, 10 and 6
- Minute 2: Node 5
- Minute 3: Node 4
- Minute 4: Nodes 9 and 2
It takes 4 minutes for the whole tree to be infected so we return 4.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/25/image-20220625231812-2.png" style="width: 75px; height: 66px;" />
<pre>
<strong>Input:</strong> root = [1], start = 1
<strong>Output:</strong> 0
<strong>Explanation:</strong> At minute 0, the only node in the tree is infected so we return 0.
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
	<li>Each node has a <strong>unique</strong> value.</li>
	<li>A node with a value of <code>start</code> exists in the tree.</li>
</ul>

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def amountOfTime(self, root: Optional[TreeNode], start: int) -> int:
        def findingnode(root,start):
            qu=[root]
            while qu:
                for i in range(len(qu)):
                    if qu[0].val==start:
                        return qu[0]
                    if qu[0].left:
                        qu.append(qu[0].left)
                    if qu[0].right:
                        qu.append(qu[0].right)
                    qu.pop(0)
        def parents(root,hash1):
            if root==None:
                return
            else:
                if root.left:
                    hash1[root.left]=root
                    parents(root.left,hash1)
                if root.right:
                    hash1[root.right]=root
                    parents(root.right,hash1)
                return
        def ans(node,hash1):
            qu=[node]
            count=-1
            hash2={}
            while qu:
                x=len(qu)
                for i in range(x):
                    if qu[0].left and qu[0].left not in hash2:
                        hash2[qu[0].left]=True
                        qu.append(qu[0].left)
                    if qu[0].right and qu[0].right not in hash2:
                        hash2[qu[0].right]=True
                        qu.append(qu[0].right)
                    if qu[0] in hash1 and hash1[qu[0]] not in hash2:
                        hash2[hash1[qu[0]]]=True
                        qu.append(hash1[qu[0]])      
                    hash2[qu[0]]=True
                    qu.pop(0)
                count+=1
            return count                     
        hash1={}
        parents(root,hash1)
        node=findingnode(root,start)
        return ans(node,hash1)                

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