#1332

Easy

auto_awesomeTwo-pointer scanning with invariant tracking

LeetCode Problem Workspace

Remove Palindromic Subsequences

This problem challenges you to remove palindromic subsequences from a string with a minimum number of steps using two-pointer scanning.

two pointers string

Problem Statement

You are given a string s that consists only of the characters 'a' and 'b'. In each step, you can remove one palindromic subsequence from the string. A subsequence can be formed by deleting some characters without rearranging the remaining characters, and it does not have to be contiguous.

Your task is to return the minimum number of steps required to make the string empty by repeatedly removing palindromic subsequences. You can optimize the number of operations based on whether the string is already a palindrome or how the characters are distributed.

Examples

Example 1

Input: s = "ababa"

Output: 1

s is already a palindrome, so its entirety can be removed in a single step.

Example 2

Input: s = "abb"

Output: 2

"abb" -> "bb" -> "". Remove palindromic subsequence "a" then "bb".

Example 3

Input: s = "baabb"

Output: 2

"baabb" -> "b" -> "". Remove palindromic subsequence "baab" then "b".

Constraints

1 <= s.length <= 1000
s[i] is either 'a' or 'b'.

Solution Approach

Two-pointer scanning for palindrome check

Use two pointers to check if the string is already a palindrome. If it is, the entire string can be removed in one step. This check is quick and helps avoid unnecessary iterations.

Character analysis for efficient subsequences

Given that the string consists only of two characters ('a' and 'b'), identify if the string can be reduced by removing palindromic subsequences that span the entire string in two steps (e.g., 'abb' -> 'bb' -> ''). This takes advantage of the problem's inherent simplicity.

Invariant tracking for optimal decisions

Track the invariant properties of the string (such as its length or structure) to decide whether removing a subsequence in one or two steps is optimal. This minimizes the number of operations required, especially when the string isn't initially a palindrome.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the final approach, typically O(n) for checking if the string is a palindrome or for scanning it with two pointers. The space complexity is O(1) as only a constant amount of extra space is used during the scan.

What Interviewers Usually Probe

The candidate efficiently uses two-pointer scanning to check if the string is a palindrome.
The candidate is able to simplify the problem by recognizing the characteristics of the string (only 'a' and 'b').
The candidate demonstrates awareness of the optimal number of steps needed based on the structure of the string.

Common Pitfalls or Variants

Common pitfalls

Failing to recognize that a string already being a palindrome can reduce the problem to a single step.
Overcomplicating the solution by not leveraging the fact that only two characters are involved, leading to inefficient checks.
Misunderstanding the requirement to remove subsequences, resulting in an incorrect approach to subsequence deletion.

Follow-up variants

What if the string contains more than two distinct characters? The problem would involve different strategies to handle subsequences.
What if the string is initially empty? The answer would trivially be 0 steps.
What if the string contains alternating patterns? The solution might involve a different set of subsequence removals.

FAQ

How does the two-pointer approach work in solving the Remove Palindromic Subsequences problem?

The two-pointer approach checks whether the string is a palindrome by comparing characters from both ends. If they match, the string is a palindrome, and it can be removed in one step.

What is the minimum number of steps for a string that is already a palindrome?

If the string is already a palindrome, the minimum number of steps required is 1, as the entire string can be removed in a single operation.

Can the problem be solved in a more efficient way if the string contains only 'a' and 'b'?

Yes, recognizing that the string contains only two characters allows for optimization, as the problem can often be reduced to just checking if the string is a palindrome and removing subsequences efficiently.

How do you handle strings that are not palindromes in the Remove Palindromic Subsequences problem?

If the string is not a palindrome, it can generally be removed in two steps: remove one subsequence, then the remainder in the next step.

What is the best approach for handling the Remove Palindromic Subsequences problem in an interview setting?

The best approach is to quickly identify if the string is a palindrome, then use two-pointer scanning and invariant tracking to decide how many steps are needed, ensuring minimal computation.

terminal

Solution

Solution 1

#### Python3

1

2

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class Solution:
    def removePalindromeSub(self, s: str) -> int:
        return 1 if s[::-1] == s else 2

Continue Practicing

#1455 check if a word occurs as a prefix of any word in a sentence #1163 last substring in lexicographical order #1147 longest chunked palindrome decomposition