Find the Kth smallest odd length palindrome number

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++

 `// C++ program for the above approach` `#include ` `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

 ``

Output:

`50405`

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

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