# Help me define solution steps for given problem

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

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?

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!

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

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