Given a positive integer K, the task is to find Kth smallest palindromic number odd length.
Examples:
Input: K = 5
Output: 5
Explanation:
The palindromic numbers of odd lengths is {1, 2, 3, 4, 5, 6, 7, …, }. The 5th smallest palindromic numbers is 5.Input: K = 10
Output: 101
Approach: The given problem can be solved based on the following observations:
- The first Palindromic Numbers of length 1 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- The first Palindromic Numbers of length 3 is 101, which is the 10th smallest odd length palindrome number. Similarly, 11th, 12th, 13th, …, 99th smallest palindromic numbers are 111, 121, 131 …, 999 respectively.
- Therefore, the Kth smallest odd length palindrome number can be formed by joining K and the reverse of K except the last digit.
From the above observations, the Kth smallest odd length palindromic number is given by appending the reverse of all the digits of K except the last one at the end of K.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the Kth smallest // odd length palindrome int oddLengthPalindrome( int k)
{ // Store the original number K
int palin = k;
// Removing the last digit of K
k = k / 10;
// Generate the palindrome by
// appending the reverse of K
// except last digit to itself
while (k > 0)
{
// Find the remainder
int rev = k % 10;
// Add the digit to palin
palin = (palin * 10) + rev;
// Divide K by 10
k = k / 10;
}
// Return the resultant palindromic
// number formed
return palin;
} // Driver Code int main()
{ int k = 504;
cout << oddLengthPalindrome(k);
} // This code is contributed by rishavmahato348 |
// Java program for the above approach import java.util.*;
import java.lang.*;
class GFG{
// Function to find the Kth smallest // odd length palindrome static int oddLengthPalindrome( int k)
{ // Store the original number K
int palin = k;
// Removing the last digit of K
k = k / 10 ;
// Generate the palindrome by
// appending the reverse of K
// except last digit to itself
while (k > 0 )
{
// Find the remainder
int rev = k % 10 ;
// Add the digit to palin
palin = (palin * 10 ) + rev;
// Divide K by 10
k = k / 10 ;
}
// Return the resultant palindromic
// number formed
return palin;
} // Driver Code public static void main(String[] args)
{ int k = 504 ;
System.out.println(oddLengthPalindrome(k));
} } // This code is contributed by Sudhanshu Bhagat & Govind Choudhary |
# Python3 program for the above approach # Function to find the Kth smallest # odd length palindrome number def oddLengthPalindrome(K):
# Store the original number K
palin = K
# Removing the last digit of K
K = K / / 10
# Generate the palindrome by
# appending the reverse of K
# except last digit to itself
while (K > 0 ):
# Find the remainder
rev = K % 10
# Add the digit to palin
palin = palin * 10 + rev
# Divide K by 10
K = K / / 10
# Return the resultant palindromic
# number formed
return palin
# Driver Code if __name__ = = '__main__' :
K = 504
print (oddLengthPalindrome(K))
#Contributed by Govind Choudhary & Pallav Pushparaj |
// C# program for the above approach using System;
class GFG{
// Function to find the Kth smallest // palindrome of odd length static int oddLengthPalindrome( int k)
{ // Store the original number K
int palin = k;
// Removing the last digit of K
k = k / 10;
// Generate the palindrome by
// appending the reverse of K
// except last digit to itself
while (k > 0)
{
// Find the remainder
int rev = k % 10;
// Add the digit to palin
palin = (palin * 10) + rev;
// Divide K by 10
k = k / 10;
}
// Return the resultant palindromic
// number formed
return palin;
} // Driver Code static void Main( string [] args)
{ int k = 504;
Console.WriteLine(oddLengthPalindrome(k));
} } // This code is contributed by Sudhanshu Bhagat & Govind Choudhary |
<script> // JavaScript program for the above approach // Function to find the Kth smallest // odd length palindrome function oddLengthPalindrome(k)
{ // Store the original number K
let palin = k;
// Removing the last digit of K
k = Math.floor(k / 10);
// Generate the palindrome by
// appending the reverse of K
// except last digit to itself
while (k > 0)
{
// Find the remainder
let rev = k % 10;
// Add the digit to palin
palin = (palin * 10) + rev;
// Divide K by 10
k = Math.floor(k / 10);
}
// Return the resultant palindromic
// number formed
return palin;
} // Driver Code let k = 504;
document.write(oddLengthPalindrome(k));
// This code is contributed by sanjoy_62. </script> |
50405
Time Complexity: O(log10K)
Auxiliary Space: O(1)