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Remove Palindromic Subsequences

Number: 1454

Difficulty: Easy

Paid? No

Companies: Amazon

Problem Description

Given a string s consisting only of letters 'a' and 'b', you can remove any palindromic subsequence in one step. The goal is to determine the minimum number of steps required to remove all characters from s. A subsequence is formed by deleting zero or more characters without changing the order, and a palindrome reads the same backwards as forwards.

Key Insights

  • Only two characters ('a' and 'b') are present.
  • Any string that is a palindrome can be removed in one step.
  • If the string is not a palindrome, it can always be emptied in 2 steps by removing all 'a's in one move and all 'b's in another.

Space and Time Complexity

Time Complexity: O(n) where n is the length of the string (to check if the string is a palindrome) Space Complexity: O(1)

Solution

The solution is straightforward:

  1. Check if the string s is empty; if so, return 0 steps.
  2. Check if s is a palindrome - if yes, return 1 step since the entire string can be removed.
  3. Otherwise, return 2 steps because you can first remove all occurrences of one character (all 'a's) as a palindromic subsequence and then remove all occurrences of the other character (all 'b's).

This approach leverages the simple structure of the string that only contains two distinct characters, thereby ensuring that any non-palindromic string can be emptied with two removals.

Code Solutions

# Function to remove palindromic subsequences
def remove_palindromic_subsequences(s: str) -> int:
    # Base case: If string is empty, return 0
    if not s:
        return 0
    # Check if the string is a palindrome
    if s == s[::-1]:
        return 1
    # Otherwise, it must be 2 (removing all 'a's and then all 'b's)
    return 2

# Example usage:
s = "abb"
print(remove_palindromic_subsequences(s))  # Output: 2
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