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Remove Palindromic Subsequences

Difficulty: Easy

Problem Description

You are given a string s consisting only of letters 'a' and 'b'. In a single step you can remove one palindromic subsequence from s. Return the minimum number of steps to make the given string empty.

Key Insights

  • A string is a palindrome if it reads the same backward as forward.
  • The entire string can be removed in one step if it is already a palindrome.
  • If the string is not a palindrome, it can be cleared in at most two steps: one for each character type ('a' and 'b').
  • The problem can be solved efficiently by checking if the string is a palindrome.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the string, for checking if the string is a palindrome. Space Complexity: O(1), as we use a constant amount of space to store variables.

Solution

To solve the problem, we can use a two-pointer approach to determine if the string is a palindrome. The algorithm follows these steps:

  1. Initialize two pointers, one at the beginning (left) and one at the end (right) of the string.
  2. Move the pointers towards the center, comparing the characters at each position.
  3. If all characters match, the string is a palindrome, and we can return 1.
  4. If any characters do not match, return 2, as we can remove 'a's and 'b's in two separate steps.

Code Solutions

def removePalindromeSub(s: str) -> int:
    # Check if the string is a palindrome
    if s == s[::-1]:
        return 1  # It is a palindrome, remove in one step
    else:
        return 2  # Not a palindrome, remove in two steps
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