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Largest and Smallest N-digit Octal Numbers
  • Last Updated : 08 Apr, 2021

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

Input: N = 4 
Output: 
Largest: 7777 
Smallest: 1000
Input: N = 2 
Output: 
Largest: 77 
Smallest: 10 
 

 

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 Octal number system is ‘7‘. Therefore: 
     
1 Digit Largest Number: '7'
2 Digit Largest Number: '77'
3 Digit Largest Number: '777'
                .
                .
                .
N Digit Largest Number: '777....(N) times'
  •  
  • Smallest Number: The smallest number in Octal 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 Octal Number System
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the largest
// N-digit number in Octal
// Number System
string findLargest(int N)
{
    // Append '7' N times
    string largest = string(N, '7');
 
    return largest;
}
 
// Function to return the smallest
// N-digit number in Octal
// 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 Octal number
void printLargestSmallest(int N)
{
    cout << "Largest: "
         << findLargest(N) << endl;
    cout << "Smallest: "
         << findSmallest(N) << endl;
}
 
// Driver code
int main()
{
    int N = 4;
 
    // Function Call
    printLargestSmallest(N);
 
    return 0;
}

Java




// Java program to find the largest
// and smallest N-digit numbers
// in Octal Number System
class GFG
{
  
// Function to return the largest
// N-digit number in Octal
// Number System
static String findLargest(int N)
{
    // Append '7' N times
    String largest = strings(N, '7');
  
    return largest;
}
  
// Function to return the smallest
// N-digit number in Octal
// Number System
static String findSmallest(int N)
{
    // Append '0' (N - 1) times to 1
    String smallest
        = "1"
          + strings((N - 1), '0');
  
    return smallest;
}
  
private static String strings(int N, char c) {
    String temp ="";
    for(int i= 0; i < N; i++) {
        temp+=c;
    }
    return temp;
}
 
// Function to print the largest and
// smallest N-digit Octal number
static void printLargestSmallest(int N)
{
    System.out.print("Largest: "
         + findLargest(N) +"\n");
    System.out.print("Smallest: "
         + findSmallest(N) +"\n");
}
  
// Driver code
public static void main(String[] args)
{
    int N = 4;
  
    // Function Call
    printLargestSmallest(N);
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python program to find the largest
# and smallest N-digit numbers
# in Octal Number System
 
# Function to return the largest
# N-digit number in Octal
# Number System
def findLargest(N):
 
    # Append '7' N times
    largest = strings(N, '7');
    return largest;
 
# Function to return the smallest
# N-digit number in Octal
# Number System
def findSmallest(N):
 
    # Append '0' (N - 1) times to 1
    smallest = "1" + strings((N - 1), '0');
    return smallest;
 
def strings(N, c):
    temp = "";
    for i in range(N):
        temp += c;
    return temp;
 
# Function to prthe largest and
# smallest N-digit Octal number
def printLargestSmallest(N):
    print("Largest: ",findLargest(N));
    print("Smallest: ",findSmallest(N));
 
# Driver code
if __name__ == '__main__':
    N = 4;
 
    # Function Call
    printLargestSmallest(N);
 
# This code is contributed by sapnasingh4991

C#




// C# program to find the largest
// and smallest N-digit numbers
// in Octal Number System
using System;
 
class GFG
{
   
// Function to return the largest
// N-digit number in Octal
// Number System
static String findLargest(int N)
{
    // Append '7' N times
    String largest = strings(N, '7');
   
    return largest;
}
   
// Function to return the smallest
// N-digit number in Octal
// Number System
static String findSmallest(int N)
{
    // Append '0' (N - 1) times to 1
    String smallest
        = "1"
          + strings((N - 1), '0');
   
    return smallest;
}
   
private static String strings(int N, char c) {
    String temp ="";
    for(int i= 0; i < N; i++) {
        temp+=c;
    }
    return temp;
}
  
// Function to print the largest and
// smallest N-digit Octal number
static void printLargestSmallest(int N)
{
    Console.Write("Largest: "
         + findLargest(N) +"\n");
    Console.Write("Smallest: "
         + findSmallest(N) +"\n");
}
   
// Driver code
public static void Main(String[] args)
{
    int N = 4;
   
    // Function Call
    printLargestSmallest(N);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// Javascript program to find the largest
// and smallest N-digit numbers
// in Octal Number System
 
// Function to return the largest
// N-digit number in Octal
// Number System
function findLargest(N)
{
    // Append '7' N times
    var largest = new Array(N+1).join( '7' );
    return largest;
}
 
// Function to return the smallest
// N-digit number in Octal
// Number System
function findSmallest(N)
{
    // Append '0' (N - 1) times to 1
    var smallest
        = "1"
          + new Array(N).join( '0' );
 
    return smallest;
}
 
// Function to print the largest and
// smallest N-digit Octal number
function printLargestSmallest(N)
{
    document.write("Largest: "
         + findLargest(N) + "<br>");
 
    document.write( "Smallest: "
         + findSmallest(N));
}
 
// Driver code
var N = 4;
// Function Call
printLargestSmallest(N);
 
</script>
Output: 
Largest: 7777
Smallest: 1000

 

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

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