Solution Explanation: Valid Palindrome II

The problem asks whether a given string can become a palindrome by removing at most one character. The optimal solution leverages a two-pointer approach with a helper function for palindrome checking.

Approach:

1. Two Pointers: The main part of the solution uses two pointers, i and j, initialized to the start and end of the string, respectively. These pointers move inwards, comparing characters at each position.

2. Mismatch Handling: If a mismatch (s[i] != s[j]) is found, it means we need to potentially remove one character to make it a palindrome. We have two possibilities: remove s[i] or remove s[j].

3. Helper Function (check): A helper function, check(i, j), efficiently determines if a substring (from index i to j) is a palindrome. This avoids redundant palindrome checks.

4. Recursive Calls: If a mismatch occurs, we recursively call check twice:

   • check(i + 1, j): Checks if the substring after removing s[i] is a palindrome.
   • check(i, j - 1): Checks if the substring after removing s[j] is a palindrome.

5. Return Value: The function returns true if either of the recursive calls returns true (meaning a palindrome can be formed by removing at most one character), or if the loop completes without finding a mismatch (the string is already a palindrome).

Time Complexity: O(n) - The algorithm iterates through the string at most twice in the worst case (one for the main loop, and one for the helper function called once or twice).

Space Complexity: O(1) - The algorithm uses a constant amount of extra space.

Code Examples (Python):

class Solution:
    def validPalindrome(self, s: str) -> bool:
        def check(i, j):
            while i < j:
                if s[i] != s[j]:
                    return False
                i, j = i + 1, j - 1
            return True
 
        i, j = 0, len(s) - 1
        while i < j:
            if s[i] != s[j]:
                return check(i + 1, j) or check(i, j - 1)  # Try removing either char
            i, j = i + 1, j - 1
        return True  # Already a palindrome

The other language examples follow a similar structure, adapting the syntax to their respective languages. The core logic remains consistent across all implementations.