1437. Minimum Insertion Steps to Make a String Palindrome

Hard
String
Dynamic Programming

Description

Given a string s. In one step you can insert any character at any index of the string.

Return the minimum number of steps to make s palindrome.

Palindrome String is one that reads the same backward as well as forward.

 

Example 1:

Input: s = "zzazz"
Output: 0
Explanation: The string "zzazz" is already palindrome we do not need any insertions.

Example 2:

Input: s = "mbadm"
Output: 2
Explanation: String can be "mbdadbm" or "mdbabdm".

Example 3:

Input: s = "leetcode"
Output: 5
Explanation: Inserting 5 characters the string becomes "leetcodocteel".

 

Constraints:

  • 1 <= s.length <= 500
  • s consists of lowercase English letters.

Hints

Hint 1
Is dynamic programming suitable for this problem ?
Hint 2
If we know the longest palindromic sub-sequence is x and the length of the string is n then, what is the answer to this problem? It is n - x as we need n - x insertions to make the remaining characters also palindrome.

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