Finding the longest palindrome in the string RACECAR. A cell (i, j) corresponds to a substring S[i…j] . For example, cell (1, 5) corresponds to Substring RACEC.
The table will be filled by filling each cell in a row starting from the bottom row and then moving to the next row above. At each step if a substring is found to be palindrome, it’s length can be compared to the maximum length string seen so far.

• Each single letter substring is a palindrome by definition.
• Each double letter substring can be readily checked to be a palindrome.
• A string S[i…j] is a palindrome if both S[i] = S[j] and S[i+1…j-1] is a palindrome. The S[i+1…j-1] string is the string obtained by removing the first and the last letters of the S[i..j] string. It corresponds to the cell diagonally below the S[i…j] string.

The highlighted cell is the maximum length Palindromic substring. In this case it is the string itself. :)