One of the solution for finding the longest palindromic substring could not be understood

Question

Refer to this article on leetcode, there's a common mistake for solving the longest palindromic substring problem:

Reverse S and become S’. Find the longest common substring between S and S’, which must also be the longest palindromic substring.

For instance:

S = “abacdfgdcaba”, S’ = “abacdgfdcaba”.

The longest common substring between S and S’ is “abacd”. Clearly, this is not a valid palindrome.

But the following rectification I could not understand well. Could anyone explain it with an step-by-step procedure/example? Thanks!

To rectify this, each time we find a longest common substring candidate, we check if the substring’s indices are the same as the reversed substring’s original indices.

Answer 1

I am stuck there, so I google to reach here. Now I understand.Let me take original String which the author mentioned as a example.

S = "caba', S' = "abac", so longest common substring is aba.

The sentence is "we check if the substring’s indices are the same as the reversed substring’s original indices."

1.What is the substring’s indices?

"aba" is [1, 2, 3]

2.what is reversed substring’s original indices? Reversed substring is "aba", and its original indices is also [1, 2, 3].

So that answer is correct.

And we are looking at another example.

S="abacdfgdcaba", S' = "abacdgfdcaba", so longest common substring is "abacd".

So same process:

1.What is the substring’s indices?

"abacd" is [0, 1, 2, 3, 4].

2.what is reversed substring’s original indices? Reversed substring is "abacd", but its original indices is also [7, 8, 9, 10, 11]. So These two "abacd" is not same one, the answer is not correct.

I think that sentence is a bit tricky, and I think the author made it a little hard to understand. ​

I think the sentence should be changed to "To rectify this, each time we find a longest common substring candidate, we check if the substring are the same one as the reversed substring’." ​