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++
// C++ implementation of the above approach#include <bits/stdc++.h>using namespace std;// Function to print the smallest and largest// palindrome with N digitsvoid 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 Codeint main(){ int n = 4; printPalindrome(n); return 0;} |
Java
// 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); } } |
Python3
# Python 3 implementation of the above approachfrom math import pow# Function to print the smallest and largest# palindrome with N digitsdef 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 Codeif __name__ == '__main__': n = 4 printPalindrome(n)# This code is contributed by# Surendra_Gangwar |
C#
// C# implementation of the approachusing 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 */ |
PHP
<?php// PHP implementation of the above approach// Function to print the smallest and largest// palindrome with N digitsfunction printPalindrome($n){ if ($n == 1) { echo "Smallest Palindrome: 0\n"; echo "Largest Palindrome: 9"; } else { echo "Smallest Palindrome: ", pow(10, $n - 1) + 1; echo "\nLargest Palindrome: ", pow(10, $n) - 1; }}// Driver Code$n = 4;printPalindrome($n);// This code is contributed by ihritik?> |
Javascript
<script> // Javascript implementation of the above approach // Function to print the smallest and largest // palindrome with N digits function printPalindrome(n) { if (n == 1) { document.write("Smallest Palindrome: 0<br>"); document.write("Largest Palindrome: 9"); } else { document.write("Smallest Palindrome: " + (parseInt(Math.pow(10, n - 1)) + 1)); document.write("<br>Largest Palindrome: " + parseInt(Math.pow(10, n) - 1)); } } // Driver Code var n = 4; printPalindrome(n);// This code is contributed by rrrtnx. </script> |
Output:
Smallest Palindrome: 1001 Largest Palindrome: 9999
Time Complexity: O(logn)
Auxiliary Space: O(1)
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