Problem Statement
Palindrome Maker
You are a text editor working on a new feature that helps users create palindromes from their input text. A palindrome is a string that reads the same forward and backward. For example, "racecar" and "level" are palindromes.
Given a string s, your task is to find the minimum number of characters you need to insert into the string to make it a palindrome. You can insert characters anywhere in the string.
For example, if the input string is "ab", you can insert "a" at the end to get "aba", which is a palindrome. So the minimum number of insertions needed is 1.
Examples
Example 1:
Input: s = "zzazz"
Output: 0
Explanation: The string is already a palindrome, so no insertions are needed.
Example 2:
Input: s = "mbadm"
Output: 2
Explanation: Insert 'b' and 'a' to get 'mbadabm'. Note that there are multiple ways to get a palindrome (e.g., 'mdbabdm'), but the minimum number of insertions is always 2.
Example 3:
Input: s = "leetcode"
Output: 5
Explanation: Insert 'e', 'd', 'o', 'c', and 'e' to get 'leetcodocteel'.
Constraints
- 1 <= s.length <= 500
- s consists of lowercase English letters.
Problem Breakdown
To solve this problem, we need to:
- The key insight is that the minimum number of insertions needed is related to the longest palindromic subsequence (LPS) of the string.
- If we find the LPS of length k in a string of length n, then we need to insert n - k characters to make the entire string a palindrome.
- We can use dynamic programming to find the LPS of the string.
- Alternatively, we can directly compute the minimum insertions needed using dynamic programming.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Palindrome Maker
You are a text editor working on a new feature that helps users create palindromes from their input text. A palindrome is a string that reads the same forward and backward. For example, "racecar" and "level" are palindromes.
Given a string s, your task is to find the minimum number of characters you need to insert into the string to make it a palindrome. You can insert characters anywhere in the string.
For example, if the input string is "ab", you can insert "a" at the end to get "aba", which is a palindrome. So the minimum number of insertions needed is 1.
Examples
Example 1:
The string is already a palindrome, so no insertions are needed.
Example 2:
Insert 'b' and 'a' to get 'mbadabm'. Note that there are multiple ways to get a palindrome (e.g., 'mdbabdm'), but the minimum number of insertions is always 2.
Example 3:
Insert 'e', 'd', 'o', 'c', and 'e' to get 'leetcodocteel'.
Problem Breakdown
Constraints:
- 1 <= s.length <= 500
- s consists of lowercase English letters.
Key Insights:
The key insight is that the minimum number of insertions needed is related to the longest palindromic subsequence (LPS) of the string.
If we find the LPS of length k in a string of length n, then we need to insert n - k characters to make the entire string a palindrome.
We can use dynamic programming to find the LPS of the string.
Alternatively, we can directly compute the minimum insertions needed using dynamic programming.
Real-World Application
This problem has several practical applications:
Text Processing
Creating palindromes for text-based puzzles or word games.
String Transformation
Transforming strings with minimal operations for data normalization.
Error Correction
Correcting errors in transmitted data by making it palindromic for redundancy.