Maximum number on 7-segment display using N segments : Recursive

Given an integer N, the task is to find the largest number that can be shown with the help of N segments using any number of 7 segment displays.

Examples:

Input: N = 4
Output: 11
Explanation:
Largest number that can be displayed with the help of 4 segments using 2 seven segment displays turned is 11.

Input: N = 7
Output: 711
Explanation:
Largest number that can be displayed by turning on seven segments is 711 with the help of 3 segments display set.

Approach:
The key observation in seven segment display is to turn on any number from 0 to 9 takes certain amounts of segments, which is described below:



If the problem is observed carefully, then the number N can be of two types that is even or odd and each of them should be solved separately as follows:

  • For Even: As in the above image, There are 6 numbers that can be displayed using even number of segments which is
    0 - 6
    1 - 2
    2 - 5
    4 - 4
    6 - 6
    9 - 6
    

    As it is observed number 1 uses the minimum count of segments to display a digit. Then, even the number of segments can be displayed using 1 with 2 counts of segments in each digit.

  • For Odd: As in the above image, there are 5 numbers that can be displayed using an odd number of segments which is
    3 - 5
    5 - 5
    7 - 3
    8 - 7
    

    As it is observed number 7 uses the minimum number of odd segments to display a digit. Then an odd number of segments can be displayed using 7 with 3 counts of segments in each digit.

Algorithm:

  • If the given number N is 0 or 1, then any number cannot be displayed with this much of bits.
  • If the given number N is odd then the most significant digit will be 7 and the rest of the digits can be displayed with the help of the (N – 3) segments because to display 7 it takes 3 segments.
  • If given number N is even then the most significant digit will be 1 and the rest of the digits can be displayed with the help of the (N – 2) segments because to display 1, it takes 2 segments only.
  • The number N is processed digit by digit recursively.

Explanation with Example:
Given number N be – 11

Digit (from MSB to LSB) N Largest number from N using segment Segments used Segments remaining
1 11 7 3 8
2 8 1 2 6
3 6 1 2 4
4 4 1 2 2
5 2 1 2 0

Then, the largest number will be 71111.

Below is the implementation of the above approach:

C++

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// C++ implementation to find the
// maximum number that can be 
// using the N segments in 
// N segments display
  
#include <iostream>
using namespace std;
  
// Function to find the maximum
// number that can be displayed
// using the N segments 
void segments(int n)
{
    // Condition to check base case
    if (n == 1 || n == 0) {
        return;
    }
    // Condition to check if the 
    // number is even
    if (n % 2 == 0) {
        cout << "1";
        segments(n - 2);
    }
      
    // Condition to check if the
    // number is odd
    else if (n % 2 == 1) {
  
        cout << "7";
        segments(n - 3);
    }
}
  
// Driver Code
int main()
{
    int n;
    n = 11;
    segments(n);
    return 0;
}

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Java

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// Java implementation to find the 
// maximum number that can be 
// using the N segments in 
// N segments display 
class GFG {
      
    // Function to find the maximum 
    // number that can be displayed 
    // using the N segments 
    static void segments(int n) 
    
        // Condition to check base case 
        if (n == 1 || n == 0) { 
            return
        
        // Condition to check if the 
        // number is even 
        if (n % 2 == 0) { 
            System.out.print("1"); 
            segments(n - 2); 
        
          
        // Condition to check if the 
        // number is odd 
        else if (n % 2 == 1) { 
      
            System.out.print("7"); 
            segments(n - 3); 
        
    
      
    // Driver Code 
    public static void main (String[] args)
    
        int n; 
        n = 11
        segments(n); 
    
}
  
// This code is contributed by AnkitRai01

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Python3

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# Python3 implementation to find the 
# maximum number that can be 
# using the N segments in 
# N segments display 
  
# Function to find the maximum 
# number that can be displayed 
# using the N segments 
def segments(n) :
  
    # Condition to check base case 
    if (n == 1 or n == 0) :
        return
      
    # Condition to check if the 
    # number is even 
    if (n % 2 == 0) :
        print("1",end=""); 
        segments(n - 2); 
      
    # Condition to check if the 
    # number is odd 
    elif (n % 2 == 1) :
  
        print("7",end=""); 
        segments(n - 3); 
  
# Driver Code 
if __name__ == "__main__"
  
    n = 11
    segments(n); 
  
# This code is contributed by AnkitRai01

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C#

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// C# implementation to find the 
// maximum number that can be 
// using the N segments in 
// N segments display 
using System;
  
class GFG {
      
    // Function to find the maximum 
    // number that can be displayed 
    // using the N segments 
    static void segments(int n) 
    
        // Condition to check base case 
        if (n == 1 || n == 0) { 
            return
        
        // Condition to check if the 
        // number is even 
        if (n % 2 == 0) { 
            Console.Write("1"); 
            segments(n - 2); 
        
          
        // Condition to check if the 
        // number is odd 
        else if (n % 2 == 1) { 
      
            Console.Write("7"); 
            segments(n - 3); 
        
    
      
    // Driver Code 
    public static void Main()
    
        int n; 
        n = 11; 
        segments(n); 
    
}
  
// This code is contributed by AnkitRai01

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Output:

71111

Performance Analysis:

  • Time Complexity: As in the above approach, there is recursive call which takes O(N) time in worst case, Hence the Time Complexity will be O(N).
  • Auxiliary Space Complexity: As in the above approach, taking consideration of the stack space used in recursive call then the auxiliary space complexity will be O(N)

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