Find the Kth smallest odd length palindrome number

Given a positive integer K, the task is to find K^th 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 5^th 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, 11^th, 12^th, 13^th, …, 99^th smallest palindromic numbers are 111, 121, 131 …, 999 respectively.
• Therefore, the K^th 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)