<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>

from collections import deque

class Solution:
    def longestPath(self, parent: List[int], s: str) -> int:
        n = len(parent)
        top_1 = [1] * n
        top_2 = [1] * n
        deg = [0] * n

        # Add edges between i and parent of i
        for i in range(1, n):
            deg[parent[i]] += 1

        # Queue for topology sort
        topo = deque()
        # Calculate the max_path
        max_path = 1
        # Add the endpoints to the queue
        for i in range(1, n):
            if deg[i] == 0:
                topo.append(i)
                deg[i] -= 1

        def update_max(u, x):
            # Update the maximum two paths for each node
            nonlocal top_1, top_2
            if x >= top_1[u]:
                top_2[u], top_1[u] = top_1[u], x
            elif x >= top_2[u]:
                top_2[u] = x

        while topo and topo[0]:
            # The current node
            u = topo.popleft()
            p = parent[u]
            # Path length
            len_path = 1 + (top_1[u] if s[u] != s[p] else 0)

            # Update max paths for current node
            update_max(p, len_path)
            # If the parent degree becomes 0, add it
            deg[p] -= 1
            if deg[p] == 0:
                topo.append(p)
            # Update the answer with max between it and the best two paths in its children
            max_path = max(max_path, top_1[p] + top_2[p] - 1)

        # The length of the longest path with the required conditions
        return max_path
31875