Nth Even length Palindrome

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

1001

Time Complexity: O(n) 
Auxiliary Space: O(n)

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