How to Solve Minimum Number of Moves to Make Palindrome

This problem requires transforming a string into a palindrome by swapping adjacent characters. A greedy strategy with two-pointer scanning helps minimize the number of swaps needed. The goal is to find an efficient solution with a minimal number of moves.

Problem Statement

Given a string s consisting of lowercase English letters, you need to transform it into a palindrome. In one move, you can select any two adjacent characters and swap them. Your task is to return the minimum number of moves required to convert the string into a palindrome.

A palindrome is a string that reads the same forwards and backwards. You can swap adjacent characters multiple times, and the challenge is to determine the fewest swaps necessary to achieve a palindrome from the given string.

Examples

Example 1

Input: s = "aabb"

Output: 2

We can obtain two palindromes from s, "abba" and "baab".

• We can obtain "abba" from s in 2 moves: "aabb" -> "abab" -> "abba".
• We can obtain "baab" from s in 2 moves: "aabb" -> "abab" -> "baab". Thus, the minimum number of moves needed to make s a palindrome is 2.

Example 2

Input: s = "letelt"

Output: 2

One of the palindromes we can obtain from s in 2 moves is "lettel". One of the ways we can obtain it is "letelt" -> "letetl" -> "lettel". Other palindromes such as "tleelt" can also be obtained in 2 moves. It can be shown that it is not possible to obtain a palindrome in less than 2 moves.

Constraints

• 1 <= s.length <= 2000
• s consists only of lowercase English letters.
• s can be converted to a palindrome using a finite number of moves.

Solution Approach

Two-Pointer Approach

Using two pointers, one starting from the leftmost character and the other from the rightmost, iterate through the string to identify characters that need to be swapped to match. This greedy approach ensures that you make minimal swaps by focusing on adjacent mismatches.

Greedy Strategy

A greedy strategy ensures that at each step, you select the best possible pair of characters to swap. By focusing on local decisions, you minimize the number of moves, making this approach both optimal and efficient.

Invariant Tracking

While applying the two-pointer strategy, keep track of the invariants of the string. As characters match or swap, you maintain consistency, making sure that any modifications don't disrupt the overall goal of creating a palindrome.

Complexity Analysis

The time complexity depends on the final approach, typically O(n) for a greedy two-pointer method, where n is the length of the string. Space complexity can be O(1) if done in-place, but may vary based on the approach used.

What Interviewers Usually Probe

• Check if the candidate utilizes two-pointer scanning effectively.
• Evaluate if the candidate can explain how a greedy strategy minimizes swaps.
• Look for a clear understanding of how tracking the invariants can optimize the solution.

Common Pitfalls or Variants

Common pitfalls

• Failing to correctly implement the two-pointer approach could lead to unnecessary swaps.
• Overcomplicating the solution with additional space or inefficient algorithms.
• Not recognizing that tracking invariants can lead to more optimal swap strategies.

Follow-up variants

• Consider variations where the string length is constrained to a smaller value.
• Explore cases where there are multiple possible palindrome outcomes.
• Introduce variations where swaps must be limited to a specific number.

How GhostInterview Helps

• GhostInterview helps by providing step-by-step assistance in identifying the optimal use of two-pointer scanning for this problem.
• It helps track each decision in the greedy approach, ensuring that the strategy minimizes the number of swaps.
• GhostInterview assists with efficiently tracking invariants, ensuring the candidate’s understanding of the palindrome transformation process is clear and precise.

Topic Pages

• Two Pointers
• String
• Greedy
• Binary Indexed Tree

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FAQ

What is the minimum number of moves to make a string a palindrome?

The minimum number of moves depends on the number of adjacent swaps needed to match characters at corresponding positions using a two-pointer scanning approach.

How do you use a greedy strategy in the 'Minimum Number of Moves to Make Palindrome' problem?

A greedy strategy involves always making the optimal local decision to minimize swaps, focusing on adjacent mismatches between characters.

How does the two-pointer technique work in palindrome transformations?

The two-pointer technique involves starting from both ends of the string and comparing characters, swapping them when necessary, to build a palindrome from both ends towards the center.

Can the minimum number of swaps be achieved without using a two-pointer approach?

While other methods could potentially solve the problem, the two-pointer approach is the most efficient and commonly used strategy for minimizing swaps.

Why is tracking invariants important in this problem?

Tracking invariants ensures that the solution maintains consistency and minimizes unnecessary swaps by respecting the overall goal of creating a palindrome.