2791. Count Paths That Can Form a Palindrome in a Tree
Description
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: 8 Explanation: The valid pairs are: - All the pairs (0,1), (0,2), (1,3), (1,4) and (2,5) result in one character which is always a palindrome. - The pair (2,3) result in the string "aca" which is a palindrome. - The pair (1,5) result in the string "cac" which is a palindrome. - The pair (3,5) result in the string "acac" which can be rearranged into the palindrome "acca".
Example 2:
Input: parent = [-1,0,0,0,0], s = "aaaaa" Output: 10 Explanation: Any pair of nodes (u,v) where u < v is valid.
Constraints:
n == parent.length == s.length
1 <= n <= 105
0 <= parent[i] <= n - 1
for alli >= 1
parent[0] == -1
parent
represents a valid tree.s
consists of only lowercase English letters.
Solutions
Solution 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 |
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