Here is the Leetcode Blog Version. This is a classic problem. I write my first leetcode accepted version based on that.

Brute force + isPalindromic will run out of time.

• length 1 substring: all are palindromic
• length 2 substring: only if two char are same

What if length 3

length 3 = length 1 + two char

0 1 2 3 4
a b c b a
+   ^    
|   |
+---+    


0 1 2 4 4
a b c b a
  +   ^     
  |   |
  +---+    

• length n = inner length n - 2 is palindromic AND (first char == last char)

• P[1][3] = true means that the substring starts from index 3 and 1 char long is palindromic.
• P[5][2] = true means that the substring starts from index 2 and 5 char long is NOT palindromic.

a matrix for abcba

  0 1 2 3 4
  a b c b a
1 1 1 1 1 1
2 0 0 0 0 -
3 0 1 0 - -
4 0 0 - - -
5 1 - - - -
^
l
e
n

With the matrix, we can fill up the martix by P[len][i] = P[len -2][i + 1] && S[i] == S[i + len -1].

Note: the length 0 is useless, so just using P[len - 1] for len.