<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:
        self.node_to_parent = {}
        self.node_to_parent[root.val] = None
        if root.val == start:
            self.start_node = root
        else:
            self.start_node = None

        def map_parent(input_queue, parent):
            for n in input_queue:
                if n:
                    if n.val == start:
                        self.start_node = n
                    self.node_to_parent[n.val] = parent
                    map_parent([n.left, n.right], n)
            return

        map_parent([root.left, root.right], root)

        self.q_infection = [[self.start_node, None]]
        self.infection_level = []
        while len(self.q_infection) > 0:
            this_level = []
            current_q_len = len(self.q_infection)

            for i in range(current_q_len):
                #print(self.q_infection)
                this_node, prev_node = self.q_infection.pop(0)
                if this_node:
                    this_level.append(this_node.val)
                    if prev_node != this_node.left:
                        self.q_infection.append([
                            this_node.left, this_node])
                    if prev_node != this_node.right:
                        self.q_infection.append([
                            this_node.right, this_node])
                    if prev_node != self.node_to_parent[this_node.val]:
                        self.q_infection.append([
                            self.node_to_parent[this_node.val], this_node
                        ])
            if len(this_level) > 0:
                self.infection_level.append(this_level)
        #print(self.infection_level)
        return len(self.infection_level) - 1
        
        
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