If at all we need a comparison, we will only compare actual characters, which are at “odd” positions like 1, 3, 5, 7, etc.
Even positions do not represent a character in string, so no comparison will be preformed for even positions.
If two characters at different odd positions match, then they will increase LPS length by 2.
There are many ways to implement this depending on how even and odd positions are handled. One way would be to create a new string 1st where we insert some unique character (say #, $ etc) in all even positions and then run algorithm on that (to avoid different way of even and odd position handling). Other way could be to work on given string itself but here even and odd positions should be handled appropriately.
Here we will start with given string itself. When there is a need of expansion and character comparison required, we will expand in left and right positions one by one. When odd position is found, comparison will be done and LPS Length will be incremented by ONE. When even position is found, no comparison done and LPS Length will be incremented by ONE (So overall, one odd and one even positions on both left and right side will increase LPS Length by TWO).
LPS of string is babcbabcbaccba : abcbabcba LPS of string is abaaba : abaaba LPS of string is abababa : abababa LPS of string is abcbabcbabcba : abcbabcbabcba LPS of string is forgeeksskeegfor : geeksskeeg LPS of string is caba : aba LPS of string is abacdfgdcaba : aba LPS of string is abacdfgdcabba : abba LPS of string is abacdedcaba : abacdedcaba
This article is contributed by Anurag Singh. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 1
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 2
- Manacher's Algorithm - Linear Time Longest Palindromic Substring - Part 4
- Longest Palindromic Substring using Palindromic Tree | Set 3
- Z algorithm (Linear time pattern searching Algorithm)
- Minimum length of substring whose rotation generates a palindromic substring
- Longest Non-palindromic substring
- Longest Palindromic Substring | Set 1
- Longest Palindromic Substring | Set 2
- Suffix Tree Application 6 - Longest Palindromic Substring
- Longest palindromic string possible after removal of a substring
- Rearrange string to obtain Longest Palindromic Substring
- Find the time which is palindromic and comes after the given time
- Make palindromic string non-palindromic by rearranging its letters
- Minimum cuts required to convert a palindromic string to a different palindromic string
- Longest Increasing Subsequence using Longest Common Subsequence Algorithm
- Maximum length palindromic substring such that it starts and ends with given char
- Shortest Palindromic Substring
- Minimum size substring to be removed to make a given string palindromic
- Check if a substring can be Palindromic by replacing K characters for Q queries