Among the list of problems that often pop up during coding interviews is a category that deals with palindromes. One such problem that hones your understanding of strings and palindromes is the “Remove Palindromic Subsequences” problem on Leetcode. In this comprehensive guide, we’ll explore this problem, delve into its constraints, and outline various approaches to solving it, each with its respective time and space complexity.
The problem is defined as follows:
Given a string
s consisting only of letters ‘a’ and ‘b’. In a single step, you can remove one palindromic subsequence from
Return the minimum number of steps to make the given string empty.
Input: s = "ababa" Output: 1 Explanation: The string itself is a palindrome, so only one step is required to make it empty.
Input: s = "abb" Output: 2 Explanation: Remove the palindrome "bb" in one step, then remove the remaining "a" in another step.
Approaches to Solve the Problem
Before diving into the code, it’s essential to understand what the problem is asking. Notice that we’re talking about removing a palindromic subsequence, not a substring. In a substring, characters have to be contiguous, but in a subsequence, they don’t.
Quick Inspection Approach
Upon inspection, we notice that the string contains only ‘a’s and ‘b’s. This immediately simplifies the problem because the complexity of a more extensive character set does not apply here.
- If the string is itself a palindrome, it can be removed in just one step.
- If the string is not a palindrome but consists of both ‘a’s and ‘b’s, you can always remove all ‘a’s in one step and all ‘b’s in another step, making it two steps.
- If the string consists of only ‘a’s or only ‘b’s, it can be considered a single-character palindrome and can be removed in one step.
Here’s a Python implementation based on this observation:
def removePalindromeSub(s): if s == s[::-1]: # Check if the string is a palindrome return 1 if "a" in s and "b" in s: # Check if both 'a' and 'b' are present return 2 return 1 # If the string is not a palindrome but consists of either all 'a's or all 'b's
Time Complexity: O(N)
Space Complexity: O(1)
Why This Approach Works
To understand why this approach works, consider the constraints and the nature of the problem.
- Palindrome: The order of characters doesn’t matter in a palindrome. So, if the string itself is a palindrome, removing it is just a matter of a single step.
- Limited Character Set: The problem limits us to ‘a’ and ‘b’, making it possible to remove all ‘a’s as a palindromic subsequence and all ‘b’s as another in just two steps if the string is not already a palindrome.
- Single Character: A string with a single type of character (‘a’ or ‘b’) is itself a palindrome, and therefore, it can be removed in one step.
Edge cases are crucial for thoroughly testing the solution. For this problem, edge cases can include:
- Empty String: Though not explicitly mentioned in the problem statement, if an empty string is provided, the function should return 0 steps.
- Single-character String: Whether it’s ‘a’ or ‘b’, it’s a palindrome, so the function should return 1.
- Strings with Only One Type of Character: If the string consists of only ‘a’s or only ‘b’s, then it’s a palindrome, and it can be removed in one step.
The “Remove Palindromic Subsequences” problem serves as a good introduction to understanding palindromes, subsequences, and problem-solving techniques that involve careful observation. While the problem might look complex at first glance, a deep understanding of its constraints leads to a surprisingly straightforward solution.