1356. Minimum Number of Moves to Make Palindrome

Hard
Two Pointers
String
Greedy
Binary Indexed Tree

Description

You are given a string s consisting only of lowercase English letters.

In one move, you can select any two adjacent characters of s and swap them.

Return the minimum number of moves needed to make s a palindrome.

Note that the input will be generated such that s can always be converted to a palindrome.

 

Example 1:

Input: s = "aabb"
Output: 2
Explanation:
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
Explanation:
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.

Hints

Hint 1
Consider a greedy strategy.
Hint 2
Let’s start by making the leftmost and rightmost characters match with some number of swaps.
Hint 3
If we figure out how to do that using the minimum number of swaps, then we can delete the leftmost and rightmost characters and solve the problem recursively.

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