CSES Solution - Longest Palindrome

Prerequisite:Manacher’s Algorithm

Given a string, your task is to determine the longest palindromic substring of the string. For example, the longest palindrome in aybabtu is bab.

Example:

Input: s = aybabtu
Output: bab

Input: GeeksgfgGeeks
Output: gfg

Approach:

The idea is to use Manacher’s algorithm, which is a linear time complexity algorithm for finding the longest palindromic substring in a given string.

Lets break down the intuition into some steps:

• We'll use two arrays, oddLength[] and evenLength[], to store the lengths of the longest odd-length and even-length palindromic substrings centered at each index of the input string.
  
• Odd-Length Palindromes: First calculates the longest odd-length palindromic substring centered at each index. It uses a variable length to keep track of the current length of the palindrome. It starts from the center and expands in both directions (left and right) until it finds a mismatch or reaches the boundary of the string. The left and right variables are used to keep track of the boundaries of the current longest palindrome.
  
• Even-Length Palindromes: The process is repeated for even-length palindromes. The only difference is that the initial length is set to 0 and the expansion starts from one position to the left of the center.
  
• Finding the Longest Palindrome: After the lengths of all palindromic substrings are calculated, iterates over the oddLength and evenLength arrays to find the maximum length and the center of the longest palindromic substring.
  
• Finally, the longest palindromic substring is extracted from the input string using the substr function and returned.

Steps-by-step approach:

• Two arrays oddLength[] and evenLength[] are declared to store the lengths of the longest palindromic substrings centered at each index.
• Implement solve() function:
  • Iterates through the string to find the longest palindromic substring using Manacher's algorithm.
  • For each index i, it calculates the length of the longest odd-length palindromic substring centered at that index.
  • Then calculates the length of the longest even-length palindromic substring centered at each index.
  • Updates the lengths of palindromic substrings in the oddLength and evenLength arrays.
  • Returns the longest palindromic substring found in the input string

Below are the implementation of the above approach:

gfg

Time Complexity: O(n), where n is the length of given string
Auxiliary Space: O(n)