I have solved the easy version of the problem. But I have no idea how to solve this one. Do I require any new algorithms? Can someone please help me solve this problem?
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Learn pattern searching algorithms like Z function, KMP, etc. I used Z function to solve this question.
Can you explain a bit more in detail on how to solve this after learning pattern matching algorithms?
The problem after this will turn into "for string $$$s$$$ of length $$$n$$$, find any index $$$i$$$ ($$$2 \le i \le n$$$) such as $$$s(i, n) = s(1, n-i+1)$$$ and $$$i \le n-i+1$$$".
(Here, $$$s(i, j)$$$ means a contiguous substring of $$$s$$$ from index $$$i$$$ to index $$$j$$$, inclusively).