3327 - Check if DFS Strings Are Palindromes\.

Hard

You are given a tree rooted at node 0, consisting of n nodes numbered from 0 to n - 1. The tree is represented by an 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 node i.

Consider an empty string dfsStr, and define a recursive function dfs(int x) that takes a node x as a parameter and performs the following steps in order:

• Iterate over each child y of x in increasing order of their numbers , and call dfs(y).

• Add the character s[x] to the end of the string dfsStr.

Note that dfsStr is shared across all recursive calls of dfs.

You need to find a boolean array answer of size n, where for each index i from 0 to n - 1, you do the following:

• Empty the string dfsStr and call dfs(i).

• If the resulting string dfsStr is a palindrome , then set answer[i] to true. Otherwise, set answer[i] to false.

Return the array answer.

A palindrome is a string that reads the same forward and backward.

Example 1:

Input: parent = -1,0,0,1,1,2, s = "aababa"

Output: true,true,false,true,true,true

Explanation:

• Calling dfs(0) results in the string dfsStr = "abaaba", which is a palindrome.

• Calling dfs(1) results in the string dfsStr = "aba", which is a palindrome.

• Calling dfs(2) results in the string dfsStr = "ab", which is not a palindrome.

• Calling dfs(3) results in the string dfsStr = "a", which is a palindrome.

• Calling dfs(4) results in the string dfsStr = "b", which is a palindrome.

• Calling dfs(5) results in the string dfsStr = "a", which is a palindrome.

Example 2:

Input: parent = -1,0,0,0,0, s = "aabcb"

Output: true,true,true,true,true

Explanation:

Every call on dfs(x) results in a palindrome string.

Constraints:

• n == parent.length == s.length

• <code>1 <= n <= 10⁵</code>

• 0 <= parent[i] <= n - 1 for all i >= 1.

• parent[0] == -1

• parent represents a valid tree.

• s consists only of lowercase English letters.