<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
from collections import deque
class Solution:
    def __init__(self): 
        self.graph = {}

    def makeGraph(self, root, came_from_val): 
        if not root: 
            return 

        if root.val not in self.graph: 
            if came_from_val != -1: 
                self.graph[root.val] = [came_from_val]
            else: 
                self.graph[root.val] = []

        if came_from_val in self.graph: 
            self.graph[came_from_val].append(root.val)


        self.makeGraph(root.left, root.val) 
        self.makeGraph(root.right, root.val) 

    def amountOfTime(self, root: Optional[TreeNode], start: int) -> int:
        self.makeGraph(root, -1)

        # bfs 
        minutes = 0
        fringe = deque([[start]])
        visited = set()
        visited.add(start)
        print(self.graph)
        if not self.graph[start]: 
            return minutes

        while fringe: 
            infecteds = fringe.popleft()
            infected_in_min = []
            for infected in infecteds: 
                for node in self.graph[infected]: 
                    # check if leaf 
                    if len(self.graph[node]) == 1 and self.graph[node][0] == infected:
                        continue
                    else: 
                        if node not in visited:
                            infected_in_min.append(node)
        
                        visited.add(node)

            if infected_in_min: 
                fringe.append(infected_in_min)
                
            minutes += 1 

        return minutes 



                    



        
        
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