# Largest and Smallest N-digit Hexadecimal Numbers

Given an integer N, the task is to find the smallest and largest N-digit numbers in Hexa-Decimal Number System.

Examples:

Input: N = 4
Output:
Largest: FFFF
Smallest: 1000

Input: N = 2
Output:
Largest: FF
Smallest: 10

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The following steps can be followed to compute 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 number is ‘0‘. The idea is that the first digit needs to be as minimum as possible other than 0 which is ‘1’ and the remaining digits needs 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++

 `// C++ program to find the largest ``// and smallest N-digit numbers ``// in Hexa-Decimal Number System `` ` `#include ``using` `namespace` `std; `` ` `// Function to return the largest ``// N-digit number in Hexa-Decimal ``// Number System ``string 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 System ``string 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 number ``void` `print(``int` `largest) ``{ ``    ``cout << ``"Largest: "` `<< findLargest(largest) << endl; ``    ``cout << ``"Smallest: "` `<< findSmallest(largest) << endl; ``} `` ` `// Driver code ``int` `main() ``{ `` ` `    ``int` `N = 4; ``    ``print(N); `` ` `    ``return` `0; ``} `

## Java

 `// Java program to find the largest ` `// and smallest N-digit numbers ` `// in Hexa-Decimal Number 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) ` `    ``{ ` `        ``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

 `# 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 System  ` `def` `findLargest(N) :  ` ` `  `    ``# Append 'F' N times  ` `    ``largest ``=` `'F'``*``N ` ` `  `    ``return` `largest;  ` ` `  `# Function to return the smallest  ` `# N-digit number in Hexa-Decimal  ` `# Number System  ` `def` `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 number  ` `def` `printAns(largest) : ` ` `  `    ``print``(``"Largest: "` `, findLargest(largest));  ` `    ``print``(``"Smallest: "` `, findSmallest(largest));  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``N ``=` `4``;  ` `    ``printAns(N);  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# program to find the largest ` `// and smallest N-digit numbers ` `// in Hexa-Decimal Number System ` `using` `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 `

Output:

```Largest: FFFF
Smallest: 1000
```

Time Complexity: O(N) where N is the length of the string.

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Improved By : AnkitRai01