<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:
    ''' 
        input => treeNode, int
        output => int

        dict:{1:[5, 3], 5:[1, 4], 3:[1, 10, 6], 4:[5, 9, 2], 9:[4], 2:[4], 10:[3], 6:[3] }
    '''
    def amountOfTime(self, root: Optional[TreeNode], start: int) -> int:
        
        adj_list = self.traverse(root, {})
        
        stack = [(0, start)]
        visited = set()
        time = 0
        while(stack):
            current_time, current_node = stack.pop()
            if(current_node in visited):
                continue
            time = max(current_time, time)
            infected_nodes = adj_list.get(current_node, [])

            for node in infected_nodes:
                if(node not in visited):
                    stack.append((current_time + 1, node))
            visited.add(current_node)

        return time

    
    def traverse(self, root, adj_list):

        if(root.left):
            adj_list[root.left.val] = adj_list.get(root.left.val, []) + [root.val]
            adj_list[root.val] = adj_list.get(root.val, []) + [root.left.val]
            adj_list = self.traverse(root.left, adj_list)
        
        if(root.right):
            adj_list[root.right.val] = adj_list.get(root.right.val, []) + [root.val]
            adj_list[root.val] = adj_list.get(root.val, []) + [root.right.val]
            adj_list = self.traverse(root.right, adj_list)
        return adj_list
61327