Unique Length 3 Palindromic Subsequences

You are given a string s, return the number of unique palindromes of length three that are a subsequence of s.

Note that even if there are multiple ways to obtain the same subsequence, it is still only counted once.

A palindrome is a string that reads the same forwards and backwards.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

• For example, "ace" is a subsequence of "abcde".

Example 1:

Input: s = "aabca"

Output: 3

Explanation: The 3 palindromic subsequences of length 3 are:

• "aba" (subsequence of "aabca")
• "aaa" (subsequence of "aabca")
• "aca" (subsequence of "aabca")

Example 2:

Input: s = "adc"

Output: 0

Explanation: There are no palindromic subsequences of length 3 in "adc".

Example 3:

Input: s = "bbcbaba"

Output: 4

Explanation: The 4 palindromic subsequences of length 3 are:

• "bbb" (subsequence of "bbcbaba")
• "bcb" (subsequence of "bbcbaba")
• "bab" (subsequence of "bbcbaba")
• "aba" (subsequence of "bbcbaba")

Constraints:

• 1 <= s.length <= 100,000
• s contains only lowercase English letters.

Topics

Hash Table String Bit Manipulation Prefix Sum

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