Count Different Palindromic Subsequences

HardDynamic Programminginterval dp

Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

Given a string s made of the letters 'a', 'b', 'c' and 'd', return the number of **distinct non-empty palindromic subsequences** of s, modulo 10^9 + 7. A subsequence is obtained by deleting zero or more characters without reordering the rest. Two subsequences are counted once if they spell the same string, no matter which positions they came from. Aim for O(n^2) time.

Examples

Input: s = "bccb"
Output: 6
The distinct palindromes are "b", "c", "bb", "cc", "bcb" and "bccb".
Input: s = "aaa"
Output: 3
"a", "aa" and "aaa"; picking different positions for "aa" does not create new strings.

Constraints

  • 1 <= s.length <= 1000
  • s[i] is one of 'a', 'b', 'c', 'd'

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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