<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 Solution:
    def longestPath(self, par: List[int], label: str) -> int:
        n = len(par)
        adj = [[] for i in range(n)]
        
        for i in range(1, n):
            adj[par[i]].append(i)
            
        vis = [0]*n 
        vis[0] = 1 
        
        queue = [0]
        q = 1 
        
        ans = 1 
        
        arr = [1]*n 
        
        while q > 0:
            s = queue[-1]
            
            leaf = True
            flag = True
            
            for z in adj[s]:
                leaf = False
                if not vis[z]:
                    flag = False
                    vis[z] = 1 
                    queue.append(z)
                    q += 1
                    
            if leaf:
                queue.pop()
                q -= 1
                continue 
                
            if flag:
                curr = []
                c = 0
                
                for z in adj[s]:
                    if label[z] != label[s]:
                        c += 1 
                        curr.append(arr[z])
                        
                if c > 1:
                    curr.sort()
                    a, b = curr[-1], curr[-2]
                    
                    ans = max(ans, a+b+1)

                    mx = a 
                elif c == 1:
                    mx = curr[0] 
                else:
                    mx = 0 
                    
                arr[s] = mx+1 
                
                ans = max(ans, arr[s])
                
                queue.pop()
                q -= 1
                
        return ans
36475