<p>You are given a <strong>tree</strong> (i.e. a connected, undirected graph that has no cycles) <strong>rooted</strong> at node <code>0</code> consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>. The tree is represented by a <strong>0-indexed</strong> array <code>parent</code> of size <code>n</code>, where <code>parent[i]</code> is the parent of node <code>i</code>. Since node <code>0</code> is the root, <code>parent[0] == -1</code>.</p>

<p>You are also given a string <code>s</code> of length <code>n</code>, where <code>s[i]</code> is the character assigned to node <code>i</code>.</p>

<p>Return <em>the length of the <strong>longest path</strong> in the tree such that no pair of <strong>adjacent</strong> nodes on the path have the same character assigned to them.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/25/testingdrawio.png" style="width: 201px; height: 241px;" />
<pre>
<strong>Input:</strong> parent = [-1,0,0,1,1,2], s = &quot;abacbe&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The longest path where each two adjacent nodes have different characters in the tree is the path: 0 -&gt; 1 -&gt; 3. The length of this path is 3, so 3 is returned.
It can be proven that there is no longer path that satisfies the conditions. 
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/25/graph2drawio.png" style="width: 201px; height: 221px;" />
<pre>
<strong>Input:</strong> parent = [-1,0,0,0], s = &quot;aabc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The longest path where each two adjacent nodes have different characters is the path: 2 -&gt; 0 -&gt; 3. The length of this path is 3, so 3 is returned.
</pre>

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

<ul>
	<li><code>n == parent.length == s.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= parent[i] &lt;= n - 1</code> for all <code>i &gt;= 1</code></li>
	<li><code>parent[0] == -1</code></li>
	<li><code>parent</code> represents a valid tree.</li>
	<li><code>s</code> consists of only lowercase English letters.</li>
</ul>

class GraphNode:
    def __init__(self, char, children):
        self.char = char
        self.children = children
    
    def __repr__(self):
        return f"GraphNode({self.char})"

class Solution:
    def longestPath(self, parent: List[int], s: str) -> int:
        nodes = self.build_graph(parent, s)
        max_chain = 1

        def dfs(node, mem):
            nonlocal max_chain

            L1 = 0
            L2 = 0

            for child in node.children:
                chain_count = dfs(child, mem)
                if child.char == node.char: continue

                if chain_count >= L1:
                    L2 = L1
                    L1 = chain_count
                elif chain_count > L2:
                    L2 = chain_count
            max_chain = max(max_chain, 1 + L1 + L2)
            mem[node] = 1 + L1
            return 1 + L1 
        
        dfs(nodes[0], {})
        return max_chain

    
    def build_graph(self, parents: List[int], s: str) -> dict[int, GraphNode]:
        nodes = {}

        for i in range(len(s)):
            nodes[i] = GraphNode(s[i], [])

        for node, parent in enumerate(parents):
            if parent == -1: continue
            nodes[parent].children.append(nodes[node])
        return nodes


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