Remove Palindromic Subsequences

Remove Palindromic Subsequences

What is this problem about?

The Remove Palindromic Subsequences interview question gives you a string consisting only of the characters 'a' and 'b'. In one step, you can remove any palindromic subsequence from the string. Your goal is to return the minimum number of steps needed to make the string empty. Because you can remove a subsequence (not just a contiguous substring), this problem has a surprising and elegant mathematical answer.

Why is this asked in interviews?

Meta and Amazon ask this problem because it rewards deep mathematical insight over algorithmic complexity. On the surface, it seems like it might require dynamic programming. But recognizing that any subsequence can be chosen — not just substrings — unlocks a constant-time observation. It tests whether candidates can move from "how do I simulate this?" to "what is the true lower bound of steps?"

Algorithmic pattern used

The pattern is pure mathematical insight with two-pointer palindrome checking. Since the string only contains 'a' and 'b', there are only three possible answers:

1. 0 — the string is already empty.
2. 1 — the string is already a palindrome (remove it all in one step).
3. 2 — in step 1, remove all 'a's (they form a palindrome). In step 2, remove all 'b's. The answer is always at most 2 for any non-empty string of 'a's and 'b's.

Use a two-pointer check to determine if the string is a palindrome.

Example explanation

String: "abba" — it's a palindrome → remove in 1 step. Answer: 1.

String: "ab" — not a palindrome. Step 1: remove "a" (palindrome). Step 2: remove "b" (palindrome). Answer: 2.

String: "" — already empty. Answer: 0.

String: "aaabbb" — not a palindrome. Remove all 'a's in step 1, all 'b's in step 2. Answer: 2.

Common mistakes candidates make

• Overthinking and implementing a full DP solution when a three-case answer suffices.
• Forgetting the empty string case (answer 0).
• Not realizing the string has ONLY two characters, which bounds the answer to at most 2.
• Implementing palindrome checking incorrectly with wrong pointer initialization.

Interview preparation tip

For the Remove Palindromic Subsequences coding problem, the two-pointer string interview pattern is only needed for the palindrome check — the rest is pure logic. Before coding, derive the three cases on paper to confirm your understanding. Interviewers at Meta appreciate when candidates immediately recognize the mathematical bound and state "the answer is at most 2 for a binary-alphabet string" before writing any code. It shows mathematical maturity and problem decomposition skills.