need algorithm to find the nth palindromic number

algorithm, c++, palindrome

Solution

I'm assuming that 0110 is not a palindrome, as it is 110.

I could spend a lot of words on describing, but this table should be enough:

#Digits #Pal. Notes
   0     1     "0" only
   1     9     x     with x = 1..9
   2     9     xx    with x = 1..9
   3    90     xyx   with xy = 10..99 (in other words: x = 1..9, y = 0..9)
   4    90     xyyx  with xy = 10..99
   5   900     xyzyx with xyz = 100..999
   6   900     and so on...

Problem

consider that ``` 0 -- is the first 1 -- is the second 2 -- is the third ..... 9 -- is the 10th 11 -- is the 11th ``` what is an efficient algorithm to find the nth palindromic number?

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