Next Palindrome Using Same Digits

Next Palindrome Using Same Digits

What is this problem about?

The Next Palindrome Using Same Digits problem gives you a numeric string of even length and asks for the next palindrome that is strictly greater and uses the same multiset of digits. This hard coding problem applies the Next Permutation concept to only the first half of the palindrome, since the second half mirrors the first.

Why is this asked in interviews?

Amazon asks this to test the combination of palindrome structure understanding with the Next Permutation algorithm. The key insight — that a palindrome is fully determined by its first half — reduces the problem to finding the next permutation of the first half and mirroring it. The two pointers and string interview pattern is applied with palindrome constraints.

Algorithmic pattern used

Extract first half + apply next permutation + mirror. For a string of length 2n, extract the first n characters. Apply the Next Permutation algorithm to this half. Mirror it to get the full palindrome (first half + reverse(first half)). This gives the next palindrome using the same digits. If no next permutation exists (first half is in descending order), return "" (no solution).

Example explanation

Palindrome: "1221". First half: "12". Apply next permutation to "12": pivot at index 0 (1 < 2), swap with rightmost > 1 which is index 1 (2) → "21", no suffix to reverse. Next half = "21". Mirror: "21" + reverse("21") = "2112". Answer: "2112".

Common mistakes candidates make

• Applying next permutation to the full string (wrong — second half mirrors first).
• Not mirroring correctly (reverse the first half for the second half).
• Applying next permutation directly when the full palindrome already has a descending first half.
• Not handling the case where no larger palindrome exists.

Interview preparation tip

Palindrome construction problems often reduce to operations on just one half. If a palindrome of length 2n has the property P, you only need to work with the first n characters — the second half follows automatically. Combining this insight with the Next Permutation algorithm is a powerful technique. Practice "next greater palindrome with same digits," "largest palindrome from digits," and similar half-based construction problems to build this instinct.