Smallest and Largest Palindrome with N Digits

Given a number N. The task is to find the smallest and largest palindromic number possible with N digits.

Examples:

Input: N = 4 
Output: 
Smallest Palindrome = 1001
Largest Palindrome = 9999

Input: N = 5
Output: 
Smallest Palindrome = 10001
Largest Palindrome = 99999


Smallest N-digit Palindromic Number: On observing carefully, you will observe that for N = 1, the smallest palindromic number will be 0. And for any other value of N, the smallest palindrome will have the first and last digits as 1 and all of the digits in between as 0.

  • Case 1 : If N = 1 then answer will be 0.
  • Case 2 : If N != 1 then answer will be (10(N-1)) + 1.

Largest N-digit Palindromic Number: Similar to the above approach, you can see that the largest possible palindrome number with N-digits can be obtained by appending 9 for N times. Therefore, largest N digits palindrome number will be 10N – 1.

Below is the implementation of the above approach:

C++

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// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the smallest and largest
// palindrome with N digits
void printPalindrome(int n)
{
    if (n == 1)
    {
        cout<<"Smallest Palindrome: 0"<<endl;
        cout<<"Largest Palindrome: 9";
    }
    else
    {
        cout<<"Smallest Palindrome: "<<pow(10, n - 1) + 1;
        cout<<"\nLargest Palindrome: "<<pow(10,n) - 1;
    }
}
  
// Driver Code
int main()
{
    int n = 4;
    printPalindrome(n);
  
    return 0;
}

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Java

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// Java implementation of the above approach 
class GfG {
  
    // Function to print the smallest and largest 
    // palindrome with N digits 
    static void printPalindrome(int n) 
    
        if (n == 1
        
            System.out.println("Smallest Palindrome: 0"); 
            System.out.println("Largest Palindrome: 9"); 
        
        else
        {
            System.out.println("Smallest Palindrome: " 
                    + (int)(Math.pow(10, n - 1)) + 1); 
                      
            System.out.println("Largest Palindrome: " 
                    + ((int)(Math.pow(10,n)) - 1)); 
        
    
      
    // Driver Code 
    public static void main(String[] args) { 
        int n = 4
        printPalindrome(n); 
    

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Python3

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# Python 3 implementation of the above approach
  
from math import pow
  
# Function to print the smallest and largest
# palindrome with N digits
def printPalindrome(n):
    if (n == 1):
        print("Smallest Palindrome: 0")
        print("Largest Palindrome: 9")
    else:
        print("Smallest Palindrome:", int(pow(10, n - 1))+1)
        print("Largest Palindrome:", int(pow(10,n))-1)
      
  
# Driver Code
if __name__ == '__main__':
    n = 4
    printPalindrome(n)
  
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
using System; 
  
class GfG 
{
  
    // Function to print the smallest and largest 
    // palindrome with N digits 
    static void printPalindrome(int n) 
    
        if (n == 1) 
        
            Console.WriteLine("Smallest Palindrome: 0"); 
            Console.WriteLine("Largest Palindrome: 9"); 
        
        else
        {
            Console.WriteLine("Smallest Palindrome: "
                    + (int)(Math.Pow(10, n - 1)) + 1); 
                      
            Console.WriteLine("Largest Palindrome: "
                    + ((int)(Math.Pow(10,n)) - 1)); 
        
    
      
    // Driver Code 
    public static void Main(String[] args) 
    
        int n = 4; 
        printPalindrome(n); 
    
  
/* This code contributed by PrinciRaj1992 */

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PHP

Output:

Smallest Palindrome: 1001
Largest Palindrome: 9999

Time Complexity: O(1)



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