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Finding next smallest Palindrome Number

A Palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward for example '123321' or 'racecar'.
Given a number inorder to find the next smallest palindrome we need to consider the following cases:

  • Case 1 : if the number is less than 10 if yes then the smallest palindrome is 11.
  • Case 2 : if the number contains all digits to be 9 eg. 9 , 99 , 999 , 9999 in such case the next smallest palindrome is 11 , 101 , 1001 , 10001 as we can see it contains n+1 digits with n-1 0's between two 1's.
  • Case 3: considering if the entered number is already a palindrome then we have 2 cases to deal with 
    1. If it does not contain a 9 in its middle digits for eg 1771 or 171 in such cases it is very easy to find the next smallest palindrome you only need to add one to the middle digits so the answer for above cases is 1881 or 181.
    2. For the Second case if it contains one in the middle digits for eg. 1991 or 17971 in this case if we add 1 to 9 it becomes 10 hence to solve this we replace 9 by 0 and add on to the digits that are besides 9 so the answer will be 2002 and 13031. also if it has more than two 9's in the middle we just keep replacing them with 0's and add on to the digits besides then eg. 139999931 the answer is 140000041
  • Case 4 : if the number is not already a palindrome then we again have 2 cases to deal with let us consider we have number 18921 so we take 2 variables i and j pointing to the middle elements that are unequal (here i points 8 and j points 2 i.e the elements besides mid element in case of odd length). then we check for the following cases : 
    1. Sub-case 1: if the ith element is greater than the jth element if yes then we simple copy the left hand side to the right hand side in this case 18921 replace 21 with 81 from the left hand side so answer is 18981.
    2. Sub-case 2 : let us consider another number 12691 in this case ith element is less than the jth element hence copying left side to the right does not work hence we add one to all the digits between ith and jth element and then copy left side to the right side so the answer is 12721.

C++ Program

Sample input and output to check the program


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