Break a Palindrome - Video Solutions

Problem Overview: You are given a palindromic string and must change exactly one character so the result is not a palindrome. Among all possible results, return the lexicographically smallest string. If no valid change exists (for example, a single-character string), return an empty string.

Approach 1: Try to Replace with 'a' Early (O(n) time, O(1) space)

This greedy approach relies on lexicographic ordering. The smallest character in lowercase strings is 'a', so you try to replace the earliest non-'a' character in the first half of the string with 'a'. Only scanning the first half works because the string is already a palindrome; modifying one side automatically breaks the symmetry. Iterate from index 0 to n/2 and replace the first character that is not 'a'. If every character in that half is already 'a', change the last character to 'b' to guarantee the result is not a palindrome. This greedy rule guarantees the smallest lexicographic result while using constant extra memory. The algorithm runs in O(n) time and O(1) space and uses simple character replacement operations.

This technique fits problems focused on string manipulation where lexicographic order matters. The key insight: breaking the palindrome as early as possible minimizes the resulting string.

Approach 2: Modify Center Character Strategy (O(n) time, O(1) space)

Another way to reason about the problem is to focus on the palindrome's structure. Since the string mirrors around the center, the only safe positions to modify while preserving minimal lexicographic growth are in the left half. Iterate through the string and look for a character that can be reduced lexicographically (for example, changing it to 'a'). If every character in the left half is already minimal, modify the final character to something slightly larger such as 'b'. This guarantees the palindrome property breaks while keeping the result close to the original ordering.

The algorithm still requires a single pass through at most half the string, leading to O(n) time complexity and O(1) space. This approach highlights the greedy decision: always perform the smallest possible change that guarantees the palindrome breaks.

Problems like this frequently appear in greedy algorithms and string categories where the optimal decision can be made locally without backtracking.

Recommended for interviews: The expected interview solution is the greedy scan that replaces the first non-'a' character in the left half. It demonstrates understanding of palindrome symmetry and lexicographic ordering. Brute-force attempts that try every replacement show basic reasoning, but the greedy O(n) solution shows stronger problem-solving and pattern recognition.