Longest Palindrome : C# : Working Example : https://dotnetfiddle.net/5lq3tQ

longest_palindrome.cs

using System;

namespace PalindromeTest {
	
	/* -------
	* Table - store palindromes : Multi Dimensional Array 
	* =========
	* Checks for palindrom
	* -  Each letter will be a palindrom
	* -  -  Set this as "True" in our Table AND set the new longest palindrome
	* -  Letters that are the same and are right next to eachother " i & i + 1 "
	* -  -  Set this as "True" in our Table AND set the new longest palindrome
	* -  First and Last letter are the same AND Table[(i +1), (j -1)] is "True" in our table
	* -  -  Set this as "True" in our Table AND set the new longest palindrome
	* -------
	*/
	
	public interface IStringUtilities {
		String GetSubstring(String s, int start, int end);	
	}
	
	public class Utilities : IStringUtilities {
		
		public String GetSubstring(String s, int start, int end){
			int length = (end - start) + 1;
			
			if(end >= s.Length){
				return s.Substring(start, (s.Length -1));
			} else {
				
				return s.Substring(start, length);
			}
		}
	}
	
	public abstract class StringExtensions : IStringUtilities {
		
		private readonly IStringUtilities _u;
		
		public StringExtensions(IStringUtilities u){
			_u = u;	
		}
		
		public String GetSubstring(String s, int start, int end){
			return _u.GetSubstring(s, start, end);
		}
		
	}
	
	public class Palindrome : StringExtensions {
		
		public String chars;
		public int length;
		public bool[,] table;
		public String longest_palindrome;
		public int palindrome_length;
		
		
		public Palindrome(String val) : base(new Utilities())
		{
			this.chars = val;
			this.length = val.Length;
			this.table = new bool[this.length, this.length];
			this.longest_palindrome = "";
			this.palindrome_length = this.longest_palindrome.Length;
		}
		
		public void CheckAndSetPalidromeLevel1(int i){
			
			table[i, i] = true;
			
			if( GetSubstring(chars, i, i).Length > palindrome_length ){
				
				longest_palindrome = GetSubstring(chars, i, i);
				
			}	
		}
		
		public void CheckAndSetPalindromeLevel2(int i){
			if(chars[i] == chars[i + 1]){
				
				table[i, (i+1)] = true;
				
				if(GetSubstring(chars, i, (i + 1)).Length > length ){
					longest_palindrome = GetSubstring(chars, i, (i + 1));
				}
			}
					
		}
		
		public void CheckAndSetPalindromeGreaterThan2(int k, int i){
			
			//do not allow "j" to be larger than or equal to palindromString.Length
			int j = 0;
			
			if((i + k) < length){
				j = i + k;
			} else {
				j = length -1;
			}
			
			
			Console.WriteLine("----- test ----- \n [i, j]: [{0}, {1}], \n palindromString[i]: {2}, \n palindromString[j]: {3}, \n String : {4} \n Table : {5}", i, j, chars[i], chars[j], GetSubstring(chars, i, j), table[(i + 1),(j - 1)]);
			
			if(chars[i] == chars[j] && table[(i + 1),(j - 1)] == true){
				
				if(GetSubstring(chars, i, j).Length > palindrome_length){
					
					//Set new palindrome
					Console.WriteLine("---- NEW LONGER ----{0}", GetSubstring(chars, i, j));
					longest_palindrome = GetSubstring(chars, i, j);
				}
				
				table[i, j] = true;
				
			}	
		}
		
	}
	
	public class Program
	{
		
		public static void Main()
		{
			
			Palindrome palindrome = new Palindrome("abaxabaxabb");
			
			//Set all cells to "false" inside our table to hold values
			for(int i = 0; i < palindrome.length; i++){
				for(int k = 0; k < palindrome.length; k++){
					palindrome.table[i,k] = false;
				}
			}
			
			
			
			Console.WriteLine("----- 1");
			for(int i = 0; i < palindrome.length; i++)
			{
				
				Console.WriteLine("value: {0}, k: [{1}, {1}]", palindrome.table[i, i], i);
				
				palindrome.CheckAndSetPalidromeLevel1(i);
				
				
			}
			
			
			
			
			
			Console.WriteLine("----- 2");
			//check to see if two characters side by side are equal
			for(int i = 0; i < palindrome.length - 1; i++){
				
				Console.WriteLine("value: {0}, k: [{1}, {2}]", palindrome.table[i, (i + 1)], i, (i + 1));
				
				palindrome.CheckAndSetPalindromeLevel2(i);
				
			}
			
			
			
			
			Console.WriteLine("----- > 2");
			for(int k = 2; k < palindrome.length - 2; k++){
				 for(int i = 0; i < palindrome.length - 2; i++){
					 
					palindrome.CheckAndSetPalindromeGreaterThan2(k, i);
					 
				}
			}
			
			// ---------- DONE --------- Write out results -----------
			
			Console.WriteLine("==================== \n ");
			Console.WriteLine("Longest Palindrome is : {0}", palindrome.longest_palindrome);
			
		}
	}
}