Nth Even length Palindrome

Difficulty Level : Medium
Last Updated : 29 Apr, 2021

Given a number n as a string, find the nth even-length positive palindrome number .

Examples:

Input : n = "1"
Output : 11
1st even-length palindrome is 11 .

Input : n = "10"
Output : 1001
The first 10 even-length palindrome numbers are 11, 22, 
33, 44, 55, 66, 77, 88, 99 and 1001.

As, it is a even-length palindrome so its first half should be equal to reverse of second half and length will be 2, 4, 6, 8 …. To evaluate nth palindrome let’s just see 1st 10 even-length palindrome numbers 11, 22, 33, 44, 55, 66, 77, 88, 99 and 1001 . Here, nth palindrome is nn’ where n’ is reverse of n . Thus we just have to write n and n’ in a consecutive manner where n’ is reverse of n .

Below is the implementation of this approach.

C++

// C++ program to find n=th even length string.
#include <bits/stdc++.h>
using namespace std;
 
// Function to find nth even length Palindrome
string evenlength(string n)
{
    // string r to store resultant
    // palindrome. Initialize same as s
    string res = n;
 
    // In this loop string r stores
    // reverse of string s after the
    // string s in consecutive manner .
    for (int j = n.length() - 1; j >= 0; --j)
        res += n[j];
 
    return res;
}
 
// Driver code
int main()
{
    string n = "10";
   
    // Function call
    cout << evenlength(n);
    return 0;
}

Java

// Java program to find nth even length Palindrome
import java.io.*;
 
class GFG
{
    // Function to find nth even length Palindrome
    static String evenlength(String n)
    {
        // string r to store resultant
        // palindrome. Initialize same as s
        String res = n;
 
        // In this loop string r stores
        // reverse of string s after the
        // string s in consecutive manner
        for (int j = n.length() - 1; j >= 0; --j)
            res += n.charAt(j);
 
        return res;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        String n = "10";
       
        // Function call
        System.out.println(evenlength(n));
    }
}
 
// Contributed by Pramod Kumar

Python3

# Python3 program to find n=th even
# length string.
import math as mt
 
# Function to find nth even length
# Palindrome
 
 
def evenlength(n):
 
    # string r to store resultant
    # palindrome. Initialize same as s
    res = n
 
    # In this loop string r stores
    # reverse of string s after the
    # string s in consecutive manner .
    for j in range(len(n) - 1, -1, -1):
        res += n[j]
 
    return res
 
 
# Driver code
n = "10"
 
# Function call
print(evenlength(n))
 
# This code is contributed by
# Mohit kumar 29

C#

// C# program to find nth even
// length Palindrome
using System;
 
class GFG {
 
    // Function to find nth even
    // length Palindrome
    static string evenlength(string n)
    {
 
        // string r to store resultant
        // palindrome. Initialize same
        // as s
        string res = n;
 
        // In this loop string r stores
        // reverse of string s after
        // the string s in consecutive
        // manner
        for (int j = n.Length - 1; j >= 0; --j)
            res += n[j];
 
        return res;
    }
 
    // Driver code
    public static void Main()
    {
        string n = "10";
 
        // Function call
        Console.WriteLine(evenlength(n));
    }
}
 
// This code is contributed by vt_m.

PHP

<?php
// PHP program to find n=th even length string.
 
// Function to find nth even length Palindrome
function evenlength($n)
{
    // string r to store resultant
    // palindrome. Initialize same as s
    $res = $n;
 
    // In this loop string r stores
    // reverse of string s after the
    // string s in consecutive manner .
    for ($j = strlen($n) - 1; $j >= 0; --$j)
        $res = $res . $n[$j];
 
    return $res;
}
 
// Driver code
$n = "10";
 
// Function call
echo evenlength($n);
 
// This code is contributed by ita_c
?>

Javascript

<script>
// Javascript program to find nth even length Palindrome
     
    // Function to find nth even length Palindrome
    function evenlength(n)
    {
        // string r to store resultant
        // palindrome. Initialize same as s
        let res = n;
  
        // In this loop string r stores
        // reverse of string s after the
        // string s in consecutive manner
        for (let j = n.length - 1; j >= 0; --j)
            res += n[j];
  
        return res;
    }
     
    // Driver code
    let n = "10";
    // Function call
    document.write(evenlength(n));
     
    //This code is contributed by avanitrachhadiya2155
     
</script>

Output

Time Complexity: O(n)

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