Problem Statement

Given string s, determine whether it's possible to make a given string palindrome by removing at most one character.

A palindrome is a word or phrase that reads the same backward as forward.

Examples

1. Example 1:

   • Input: "racecar"
   • Expected Output: true
   • Justification: The string is already a palindrome, so no removals are needed.

2. Example 2:

   • Input: "abeccdeba"
   • Expected Output: true
   • Justification: Removing the character 'd' forms the palindrome "abccba".

3. Example 3:

   • Input: "abcdef"
   • Expected Output: false
   • Justification: No single character removal will make this string a palindrome.

Constraints:

• 1 <= s.length <= 10⁵
• str consists of lowercase English letters.

Solution

To solve this problem, we use a two-pointer approach that initiates at both ends of the string. These pointers move towards the center, comparing characters at each step. Upon encountering a mismatch, the algorithm decides whether to skip the character at the left or the right pointer. A helper function is used to check if the resulting substring (after skipping a character) forms a palindrome. This process is performed twice, once for each pointer. If either scenario results in a palindrome, the original string can be considered a valid palindrome after removing at most one character. This efficient method determines the feasibility of forming a palindrome with minimal alterations to the string.

1. Initialization: Begin by initializing the left pointer with 0 and the right pointer with n - 1, where n is a string length.

2. Two-Pointer Traversal: Use two pointers, and move these pointers towards the center, comparing the characters at each step.

3. Handling Mismatch: Upon encountering a mismatch, the algorithm checks two scenarios: removing the character at the left pointer or at the right pointer. For each scenario, it checks if the remaining substring forms a palindrome.

4. Greedy Decision Making: If either resulting substring is a palindrome, return true. This decision is based on the greedy principle that choosing the first viable option (resulting in a palindrome) is sufficient.

5. Concluding Result: If neither scenario results in a palindrome, the algorithm concludes that it's impossible to form a palindrome by removing just one character and returns false.

This greedy approach is efficient as it minimizes the number of checks needed to determine if the string can be a valid palindrome with a single character removal.

Algorithm Walkthrough

Input:- "abeccdeba"

1. Initial Setup:

   • Two pointers are initialized: left at the start (pointing to 'a') and right at the end (pointing to 'a').

2. First Iteration:

   • Compare characters at left and right pointers.
   • Characters are the same ('a'), so move left to the right and right to the left.

3. Second Iteration:

   • Now left points to 'b' and right points to 'b'.
   • Characters match, so move left and right inward again.

4. Third Iteration:

   • left is now at 'e', and right is at 'e'.
   • Characters match, so move left and right inward again.

5. Fourth Iteration:

   • left is now at 'c', and right is at 'd'.
   • Characters do not match. This is where a decision is made.

6. Checking Substrings:

   • Remove the character at the left pointer ('c') and check if the substring "cd" is a palindrome. It is not.
   • Remove the character at the right pointer ('d') and check if the substring "cc" is a palindrome. It is a palindrome.

7. Conclusion:

   • Since removing the character 'd' (at the right pointer) resulted in a palindrome, the answer is true.