<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, parent: List[int], s: str) -> int:
        neighbors = defaultdict(list)
        for node in range(1, len(parent)):
            if node == 0 or s[node] == s[parent[node]]:
                continue
            neighbors[node].append(parent[node])
            neighbors[parent[node]].append(node)
        
        visited = set()

        def bfs(root):
            queue = deque([(root, 1)])
            cur_visit = set()
            max_length = 0
            last_node = -1
            while queue:
                node, length = queue.popleft()
                max_length = length
                last_node = node
                cur_visit.add(node)
                visited.add(node)
                for nei in neighbors[node]:
                    if nei in cur_visit:
                        continue
                    queue.append((nei, length + 1))
            return (last_node, max_length)

        def maxPathLenContaining(node):
            # Do a BFS from node to get furthest node
            last_node, _ = bfs(node)

            # Do a second BFS from this node to get longuest path
            _, max_len = bfs(last_node)
            return max_len


        maxlen = 0
        for node in range(len(s)):
            if node in visited:
                continue
            maxlen = max(maxlen, maxPathLenContaining(node))
        return maxlen
            
            


"""
build a graph 

remove all edges that have adjacent letters

find the longuest path in the remaining subtrees 



"""
46825