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

  • Last Updated : 10 Jun, 2021

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. 
 

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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)NLargest number from N using segmentSegments usedSegments remaining
111738
28126
36124
44122
52120

Then, the largest number will be 71111.
Below is the implementation of the above approach:
 

C++




// 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;
}

Java




// 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

Python3




# 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

C#




// 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

Javascript




<script>
    // Javascript 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
    function segments(n)
    {
        // Condition to check base case
        if (n == 1 || n == 0) {
            return;
        }
        // Condition to check if the
        // number is even
        if (n % 2 == 0) {
            document.write("1");
            segments(n - 2);
        }
           
        // Condition to check if the
        // number is odd
        else if (n % 2 == 1) {
       
            document.write("7");
            segments(n - 3);
        }
    }
     
    let n;
    n = 11;
    segments(n);
 
// This code is contributed by divyesh072019.
</script>
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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