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Find the Kth smallest odd length palindrome number

  • Difficulty Level : Easy
  • Last Updated : 22 Jul, 2021

Given a positive integer K, the task is to find Kth smallest palindromic number odd length.

Examples:

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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++




// 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




// 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




# 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#




// 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

Javascript




<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>
Output: 
50405

 

Time Complexity: O(log10K)
Auxiliary Space: O(1)




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