Make String Anti-palindrome

Make String Anti-palindrome

What is this problem about?

The Make String Anti-palindrome problem gives you a string of even length. You can rearrange its characters in any order. Your goal is to return the lexicographically smallest "anti-palindrome". An anti-palindrome is a string where the character at index i is strictly not equal to the character at index n - 1 - i for all valid i.

Why is this asked in interviews?

This is a Hard-level greedy string manipulation problem. It tests a candidate's ability to apply sorting to achieve lexicographical minimums, and then systematically resolve constraint violations (the palindrome reflections). Interviewers ask this to see if you can elegantly swap elements to fix collisions without destroying the carefully constructed alphabetical order.

Algorithmic pattern used

This utilizes a Greedy / Sorting pattern.

1. First, sort the string to make it lexicographically smallest.
2. Because it's sorted, identical characters will be grouped together. Collisions (where s[i] == s[n - 1 - i]) will only happen if a single character's frequency is so large that it spans across the middle of the string.
3. To fix the collision, you find the next different character in the right half of the string and swap it into the colliding position. Since you want the smallest result, you swap the smallest available valid characters.

Example explanation

String: "aabbbb" (length 6).

1. Sort it: "aabbbb".
2. Let's check anti-palindrome conditions:
   • Index 0 ('a') vs Index 5 ('b'). Valid.
   • Index 1 ('a') vs Index 4 ('b'). Valid.
   • Index 2 ('b') vs Index 3 ('b'). Collision! s[2] == s[3].
3. We need to fix index 3. We look to the right of index 3 for a character that is NOT 'b'.
   • Index 4 is 'b'.
   • Index 5 is 'b'.
   • Wait, there are no other characters! In this specific problem context, valid inputs guarantee a solution exists, but if it didn't, it would be impossible. If we had "aabbcc", sorted is "aabbcc". Middle is b vs b. We swap the right b with the first c, resulting in "aabccb".

Common mistakes candidates make

A frequent mistake is overcomplicating the swap logic. Candidates often try to use Hash Maps and rebuild the string from scratch by placing characters left and right. This usually fails the "lexicographically smallest" requirement. Since sorting immediately gives you the lexicographically smallest base, the most efficient approach is simply to detect the collision at the middle and perform the minimal necessary swaps with the right-side elements.

Interview preparation tip

When tackling the Make String Anti-palindrome interview pattern, remember that because the string is sorted, any palindrome collision will always occur exactly at the middle of the string. You don't need to check the outer edges initially! Find where the middle elements overlap, and push the right-side overlapping elements further down the array until they hit a new character.