Largest and Smallest N-digit Hexadecimal Numbers

20 Jan, 2022
Given an integer N, the task is to find the smallest and largest N-digit numbers Hexa-Decimal Number System.
Examples: 
Input: N = 4 Output: Largest: FFFF Smallest: 1000
Input: N = 2 Output: Largest: FF Smallest: 10 
Approach: The following steps can be followed to complete the required answer: 
Largest Number: To get the largest number, every digit of the number must be maximum. The maximum digit in the Hexa-Decimal number system is ‘F‘. Therefore:
1 Digit Largest Number: 'F'
2 Digit Largest Number: 'FF'
3 Digit Largest Number: 'FFF'
                .
                .
                .
N Digit Largest Number: 'FFF....(N) times'
Smallest Number: The smallest number in hexadecimal numbers is ‘0‘. The idea is that the first digit needs to be as minimal as possible other than 0 which is ‘1’ and the remaining digits need to be 0. Therefore:
1 Digit Smallest Number: '1'
2 Digit Smallest Number: '10'
3 Digit Smallest Number: '100'
                .
                .
                .
N Digit Smallest Number: '100....(N - 1) times'
Below is the implementation of the above approach: 
C++
Java
Python3
C#
Javascript
// C++ program to find the largest// and smallest N-digit numbers// in Hexa-Decimal Number System #include <bits/stdc++.h>using namespace std; // Function to return the largest// N-digit number in Hexa-Decimal// Number Systemstring findLargest(int N){    // Append 'F' N times    string largest = string(N, 'F');     return largest;} // Function to return the smallest// N-digit number in Hexa-Decimal// Number Systemstring findSmallest(int N){    // Append '0' (N - 1) times to 1    string smallest = "1" + string((N - 1), '0');     return smallest;} // Function to print the largest and smallest// N-digit Hexa-Decimal numbervoid print(int largest){    cout << "Largest: " << findLargest(largest) << endl;    cout << "Smallest: " << findSmallest(largest) << endl;} // Driver codeint main(){     int N = 4;    print(N);     return 0;}
// Java program to find the largest// and smallest N-digit numbers// in Hexa-Decimal Number Systemclass GFG {         // Function to return the largest    // N-digit number in Hexa-Decimal    // Number System    static String findLargest(int N)    {                 String largest = "";        // Append 'F' N times        for (int i = 0; i < N ; i++)            largest += 'F';             return largest;    }         // Function to return the smallest    // N-digit number in Hexa-Decimal    // Number System    static String findSmallest(int N)    {                 String smallest = "1" ;        // Append '0' (N - 1) times to 1        for(int i = 0; i < N - 1; i++)            smallest += '0';             return smallest;    }         // Function to print the largest and smallest    // N-digit Hexa-Decimal number    static void print(int largest)    {        System.out.println("Largest: " + findLargest(largest)) ;        System.out.println("Smallest: " + findSmallest(largest)) ;    }         // Driver code    public static void main (String[] args)    {             int N = 4;        print(N);         }} // This code is contributed by AnkitRai01
# Python3 program to find the largest# and smallest N-digit numbers# in Hexa-Decimal Number System # Function to return the largest# N-digit number in Hexa-Decimal# Number Systemdef findLargest(N) :     # Append 'F' N times    largest = 'F'*N     return largest; # Function to return the smallest# N-digit number in Hexa-Decimal# Number Systemdef findSmallest(N) :     # Append '0' (N - 1) times to 1    smallest = '1' + '0'*(N - 1)     return smallest; # Function to print the largest and smallest# N-digit Hexa-Decimal numberdef printAns(largest) :     print("Largest: " , findLargest(largest));    print("Smallest: " , findSmallest(largest)); # Driver codeif __name__ == "__main__" :     N = 4;    printAns(N); # This code is contributed by AnkitRai01
// C# program to find the largest// and smallest N-digit numbers// in Hexa-Decimal Number Systemusing System; class GFG {         // Function to return the largest    // N-digit number in Hexa-Decimal    // Number System    static string findLargest(int N)    {                 string largest = "";                 // Append 'F' N times        for (int i = 0; i < N ; i++)            largest += 'F';             return largest;    }         // Function to return the smallest    // N-digit number in Hexa-Decimal    // Number System    static string findSmallest(int N)    {                 string smallest = "1" ;                 // Append '0' (N - 1) times to 1        for(int i = 0; i < N - 1; i++)            smallest += '0';             return smallest;    }         // Function to print the largest and smallest    // N-digit Hexa-Decimal number    static void print(int largest)    {        Console.WriteLine("Largest: " +                    findLargest(largest)) ;        Console.WriteLine("Smallest: " +                    findSmallest(largest)) ;    }         // Driver code    public static void Main(string[] args)    {        int N = 4;        print(N);    }} // This code is contributed by AnkitRai01
<script>// Javascipt implementation of the// above approach // Function to return the largest// N-digit number in Hexa-Decimal// Number Systemfunction findLargest(N){    // Append 'F' N times "a".repeat(10)    var largest = "F".repeat(N);       return largest;}   // Function to return the smallest// N-digit number in Hexa-Decimal// Number Systemfunction findSmallest(N){    // Append '0' (N - 1) times to 1    var smallest = "1" + "0".repeat(N-1);       return smallest;}   // Function to print the largest and smallest// N-digit Hexa-Decimal numberfunction print(largest){    document.write("Largest: " + findLargest(largest) + "<br>");    document.write("Smallest: " + findSmallest(largest) + "<br>");} // Driver codevar N = 4;print(N); // This code is contributed by Shivanisingh</script>
Largest: FFFF
Smallest: 1000
 
Time Complexity: O(N) where N is the length of the string.
Auxiliary Space: O(1) 
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