Hey Geeks I think question can be solved by many ways . some of the 
algorithms are i have implemented & aware of are ->

1st. Algo
 Generate all palindromes (even & odd length ) of given string while keep 
tracking of their length in last just compare max (evenlength_palindrome , 
oddlength_palindrome) . 
 Time Complexity O(N^2) where N is length of String

2nd . Algo. For Those Who are just saying Use DP :)
  Find The LCS(Longest Common Sub-sequence of String (say s1)& reverse of 
String (say s2) ) It Involves  
  DP to solve efficiently but guaranteed optimal solution 
  Time Complexity O(N^2) where N is length of String
  Space  Complexity O(N^2)  for table 

3rd. Use Suffix Tree ( Need to Work On It)  basic idea is to build the 
suffix tree of string & reverse string check no every node where suffix 
belongs to , the deepest common node will us longest palindrome in given 
string.

Correct me if i missed something ?

Thanks
Shashank Mani 
Computer Science
Birla Institute of Technology ,Mesra

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