Help me define solution steps for given problem

Help me define solution steps for given problem
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#1

Given a string s0 find the lexicographically smallest palindrome of the same length that is lexicographically greater than or equal tos0.

Strings may contain only lowercase English letters.

Example

  • For s0 = "cbaba", the output should be
    smallestPalindrome(s0) = "cbabc";
  • For s0 = "abcbc", the output should be
    smallestPalindrome(s0) = "abdba".

Input/Output

  • [time limit] 4000ms (js)
  • [input] string s0

A string containing only lowercase English letters.

Guaranteed constraints:
4 ≤ s0.length ≤ 5 · 10^5.

[output] string

The required palindrome.

Help me define steps in solving this algorithm I can’t recognize the pattern, so I am not sure what to do. Any clues will be helpful, I understand what is lexicographically smallest palindrome. What I don’t understand is the logic behind generating new palindrome, when can I introduce a new letter that hasn’t been part of input?


#2

You are given a string (may not be a palindrome) and you must find a palindrome of the same length which would come alphabetically after the given string (or if the input string is a palindrome, return the string itself).

So cbaba is not a palindrome. Next would be cbabb. Not a palindrome. Next - cbabc. A palindrome! Done!


#3

Ok I understood that, but what about in this case when input is “xgdfcs” and expected output is “xgeegx”?
How do you decide that 3rd letter is gonna be e and why?

or when input is “aazzzzba” and expected output is “abaaaaba”, what’s the pattern there


#4

The pattern is an alphabetical order. You keep “incrementing” the input string until you find a palindrome.