Valid Palindrome III

Valid Palindrome III

What is this problem about?

The "Valid Palindrome III" interview question is a more advanced version of the palindrome deletion problem. Instead of being allowed only one deletion, you are given an integer k and must determine if the string can be transformed into a palindrome by removing at most k characters. This is a classic optimization problem that asks for the minimum number of deletions required to achieve a palindrome.

Why is this asked in interviews?

This "Valid Palindrome III" coding problem is often seen in "Hard" difficulty rounds at Meta and TikTok. It tests whether a candidate can recognize the relationship between palindromes and the Longest Palindromic Subsequence (LPS). It requires a strong grasp of Dynamic Programming, as a greedy approach is no longer sufficient when multiple deletions are allowed.

Algorithmic pattern used

The most effective algorithmic pattern here is "Dynamic Programming (DP)." The problem can be reduced to finding the Longest Palindromic Subsequence of the string. If the length of the original string is n and the length of its LPS is L, then the minimum number of deletions needed to make it a palindrome is n - L. If n - L <= k, the answer is true.

Example explanation

Suppose the string is "abcdeca" and k = 2.

1. The string is not a palindrome.
2. We look for the Longest Palindromic Subsequence.
3. Possible palindromic subsequences: "aca", "aba", "abba" is not possible, but "aceca" is!
4. The LPS is "aceca", which has a length of 5.
5. Minimum deletions = Length(string) - Length(LPS) = 7 - 5 = 2.
6. Since 2 <= k, the result is true.

Common mistakes candidates make

Candidates often try to solve this using recursion without memoization, leading to an exponential time complexity that will time out. Another mistake is failing to see the connection to the Longest Palindromic Subsequence and instead trying to manage the state of k directly in a 3D DP table, which is more complex and less efficient than the LPS approach.

Interview preparation tip

When you see a problem asking for "at most k removals" to achieve a property, think about the "inverse" of that property. For palindromes, the inverse of removals is the Longest Palindromic Subsequence. Mastering the LPS "Dynamic Programming interview pattern" is essential for solving many related string problems.