3615 - Longest Palindromic Path in Graph.

Hard

You are given an integer n and an undirected graph with n nodes labeled from 0 to n - 1 and a 2D array edges, where <code>edgesi = u_i, v_i</code> indicates an edge between nodes <code>u_i</code> and <code>v_i</code>.

You are also given a string label of length n, where label[i] is the character associated with node i.

You may start at any node and move to any adjacent node, visiting each node at most once.

Return the maximum possible length of a palindrome that can be formed by visiting a set of unique nodes along a valid path.

Example 1:

Input: n = 3, edges = [0,1,1,2], label = "aba"

Output: 3

Exp****lanation:

• The longest palindromic path is from node 0 to node 2 via node 1, following the path 0 → 1 → 2 forming string "aba".

• This is a valid palindrome of length 3.

Example 2:

Input: n = 3, edges = [0,1,0,2], label = "abc"

Output: 1

Explanation:

• No path with more than one node forms a palindrome.

• The best option is any single node, giving a palindrome of length 1.

Example 3:

Input: n = 4, edges = [0,2,0,3,3,1], label = "bbac"

Output: 3

Explanation:

• The longest palindromic path is from node 0 to node 1, following the path 0 → 3 → 1, forming string "bcb".

• This is a valid palindrome of length 3.

Constraints:

• 1 <= n <= 14

• n - 1 <= edges.length <= n * (n - 1) / 2

• <code>edgesi == u_i, v_i</code>

• <code>0 <= u_i, v_i<= n - 1</code>

• <code>u_i != v_i</code>

• label.length == n

• label consists of lowercase English letters.

• There are no duplicate edges.