Count Paths That Can Form a Palindrome in a Tree
You are given a tree (i.e. a connected, undirected graph that has no cycles) rooted at node 0 consisting of n nodes numbered from 0 to n - 1. The tree is represented by a 0-indexed array parent of size n, where parent[i] is the parent of node i. Since node 0 is the root, parent[0] == -1.
You are also given a string s of length n, where s[i] is the character assigned to the edge between i and parent[i]. s[0] can be ignored.
Return the number of pairs of nodes (u, v) such that u < v and the characters assigned to edges on the path from u to v can be rearranged to form a palindrome.
A string is a palindrome when it reads the same backwards as forwards.
Example 1
Input
parent = [-1,0,0,1,1,2], s = "acaabc"Output
8The valid pairs are (0,1), (0,2), (1,3), (1,4), (2,5), (2,3), (1,5), and (3,5), whose path characters can be rearranged to form palindromes.
Example 2
Input
parent = [-1,0,0,0,0], s = "aaaaa"Output
10Any pair of nodes (u, v) where u < v is valid.
Constraints
- n == parent.length == s.length
- 1 <= n <= 10^5
- 0 <= parent[i] <= n - 1 for all i >= 1
- parent[0] == -1
- parent represents a valid tree.
- s consists of only lowercase English letters.