<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:
        parent={}
        res=None
        from collections import deque
        res=self.getParent(root,res,parent,start)
        return self.burnTime(root,res,parent)

    def burnTime(self,root,res,parent):
        if root==None:
            return 0
        q=deque()
        q.append(res)
        vis={}
        vis[res]=1
        
        maxTime=0
        while q:
            n=len(q)
            check=False
            for i in range(n):
                ele=q.popleft()
                if ele.left!=None and ele.left not in vis.keys():
                    check=True
                    q.append(ele.left)
                    vis[ele.left]=1

                if ele.right!=None and ele.right not in vis.keys():
                    check=True
                    q.append(ele.right)
                    vis[ele.right]=1
                
                if ele in parent.keys() and parent[ele] not in vis.keys():
                    check=True
                    q.append(parent[ele])
                    vis[parent[ele]]=1
            
            if check:
                maxTime+=1

        return maxTime
                

    
    def getParent(self,root,res,parent,start):
        if root==None:
            return None
        q=deque()
        q.append(root)
        parent[root]=root
        
        while q:
            ele=q.popleft()
            if ele.val==start:
                res=ele
            if ele.left!=None:
                q.append(ele.left)
                parent[ele.left]=ele
            if ele.right!=None:
                q.append(ele.right)
                parent[ele.right]=ele
        return res
357