N’th palindrome of K digits in C++

To find the n-th palindrome of k digits, we can iterate from the first k digits number till we find the n-th palindrome number. This approach is not efficient. You can try it yourself.

Now, let's see the efficient approach to find the n-th palindrome of k digits.

There are two halves in the numbers. The first half is equal to the reverse of the second half.

The first half of the n-th number with k digits are

If k is odd then (n - 1) + 10^k/2else(n-1)+10^k/2-1

The second half of the n-th number with k digits will be the reverse of the first half of the digits. Truncate the last digit from the first half of the number, if k is odd.

Algorithm

Initialise the numbers n and k.
Find the length of the first half of the k-digit palindrome using the value of k.
The first half of the palindrome is pow(10, length) + n - 1.
If the k is odd, then remove the last digit from the first half of the palindrome.
Reverse the first half and print the second half.

Implementation

Following is the implementation of the above algorithm in C++

#include<bits/stdc++.h>
using namespace std;
void findNthPalindrome(int n, int k) {
   int temp = (k & 1) ? (k / 2) : (k / 2 - 1);
   int palindrome = (int)pow(10, temp);
   palindrome += n - 1;
   cout << palindrome;
   if (k & 1) {
      palindrome /= 10;
   }
   while (palindrome) {
      cout << palindrome % 10;
      palindrome /= 10;
   }
      cout << endl;
}
int main(){
   int n = 7, k = 8;
   findNthPalindrome(n ,k);
   return 0;
}