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Longest Palindromic Path in Graph

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 edges[i] = [ui, vi] indicates an edge between nodes ui and vi.

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 edges[i] = [ui, vi] indicates an edge between nodes ui and vi.

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.

Longest Palindromic Path in Graph diagram

Example 1

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

Output: 3

Example 2

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

Output: 1

Example 3

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

Output: 3

Constraints

  • 1 <= n <= 14
  • n - 1 <= edges.length <= n * (n - 1) / 2
  • edges[i] == [ui, vi]
  • 0 <= ui, vi <= n - 1
  • ui != vi
  • label.length == n
  • label consists of lowercase English letters.
  • There are no duplicate edges.

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