<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 TreeNode:
    def __init__(self, val='', pos=0):
        self.val = val
        self.pos = pos
        self.children = []

class Solution:
    def longestPath(self, parent: List[int], s: str) -> int:
        # Create the tree nodes
        nodes = [TreeNode(s[i], i) for i in range(len(parent))]
        
        # Construct the tree
        for i in range(1, len(parent)):
            p = parent[i]
            nodes[p].children.append(nodes[i])

        self.ans = 0

        def dfs(node: TreeNode) -> int:
            if not node.children:
                return 1
            
            max_len = 0
            second_max_len = 0

            for child in node.children:
                child_len = dfs(child)
                
                if s[child.pos] != s[node.pos]:
                    if child_len > max_len:
                        second_max_len = max_len
                        max_len = child_len
                    elif child_len > second_max_len:
                        second_max_len = child_len

            # Update the answer with the maximum path length including this node
            self.ans = max(self.ans, max_len + second_max_len + 1)
            
            # Return the longest path length ending at this node
            return max_len + 1

        dfs(nodes[0])
        return max(dfs(nodes[0]), self.ans)

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