Complexity for two approaches of finding next biggest palindrome of a number
I did some digging on this and i think the 2nd one is more efficient. I can not determine the complexity though but i know why the first one will take more time than the 2nd one.

In the first i approach, i did some arithmatic addition on the given input directly like here a = str(int(a) + 1) or here firsthalf = str(int(firsthalf) + 1) rather than just doing arithmatic on a single number like in the 2nd approach center = str(int(center)+1). So apparently a being a huge number and doing arithmatic on it will take a considerable amount of time.

This is the easiest explanation i can come up with. If anyone can do a more elaborate explanation with the given complexity for both the algorithms please feel free to do so.