Minimum number of Binary strings to represent a Number

Given a number N. The task is to find the minimum number of binary strings required to represent the given number as the sum of the binary strings.

Examples:

Input : 131
Output : Minimum Number of binary strings needed: 3
111 10 10

Input : 564
Output :Minimum Number of binary strings needed: 6
111 111 111 111 110 10

Approach:



  • Store all digits of the given number in the array.
  • Find the maximum digit in the array. This maximum number(maxi) indicates the number of binary strings required to represent the given number.
  • Now, find maxi numbers by substuting 0’s and 1’s greadily.

Below is the implementation of the above approach:

C++

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// C++ program to find the minimum number of 
// binary strings to represent a number
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the minimum number of 
// binary strings to represent a number
void minBinary(int n)
{
    int digit[10], len = 0;
      
    while (n > 0) {
        digit[len++] = n % 10;
        n /= 10;
    }
      
    // Storing digits in correct order
    reverse(digit, digit + len); 
  
    int ans = 0;
      
    // Find the maximum digit in the array
    for (int i = 0; i < len; i++) {
        ans = max(ans, digit[i]);
    }
  
    cout << "Minimum Number of binary strings needed: "
         << ans << endl;
  
    // Traverse for all the binary strings
    for (int i = 1; i <= ans; i++) 
    {
        int num = 0;
        for (int j = 0; j < len; j++)
        {
            // If digit at jth position is greater 
            // than 0 then substitute 1
            if (digit[j] > 0) {
  
                num = num * 10 + 1;
                digit[j]--;
            }
            else {
                num *= 10;
            }
        }
        cout << num << " ";
    }
  
}
  
// Driver code
int main()
{
    int n = 564;
      
    minBinary(n);
      
    return 0;
}

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Java

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// Java program to find the minimum number of 
// binary Strings to represent a number
import java.util.*;
  
class GFG 
{
  
    // Function to find the minimum number of
    // binary Strings to represent a number
    static void minBinary(int n)
    {
        int[] digit = new int[10];
        int len = 0;
  
        while (n > 0
        {
            digit[len++] = n % 10;
            n /= 10;
        }
  
        // Storing digits in correct order
        digit = reverse(digit, 0, len - 1);
  
        int ans = 0;
  
        // Find the maximum digit in the array
        for (int i = 0; i < len; i++) 
        {
            ans = Math.max(ans, digit[i]);
        }
  
        System.out.print("Minimum Number of binary"
                   " Strings needed: " + ans + "\n");
  
        // Traverse for all the binary Strings
        for (int i = 1; i <= ans; i++)
        {
            int num = 0;
            for (int j = 0; j < len; j++) 
            {
                // If digit at jth position is greater
                // than 0 then substitute 1
                if (digit[j] > 0
                {
                    num = num * 10 + 1;
                    digit[j]--;
                }
                else
                {
                    num *= 10;
                }
            }
            System.out.print(num + " ");
        }
    }
  
    static int[] reverse(int str[], 
                         int start, int end)
    {
  
        // Temporary variable to store character
        int temp;
        while (start <= end)
        {
            // Swapping the first and last character
            temp = str[start];
            str[start] = str[end];
            str[end] = temp;
            start++;
            end--;
        }
        return str;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int n = 564;
  
        minBinary(n);
    }
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 program to find the minimum number of 
# binary strings to represent a number
  
# Function to find the minimum number of 
# binary strings to represent a number
def minBinary(n):
    digit = [0 for i in range(3)]
    len = 0
      
    while (n > 0):
        digit[len] = n % 10
        len += 1
        n //= 10
      
    # Storing digits in correct order
    digit = digit[::-1
  
    ans = 0
      
    # Find the maximum digit in the array
    for i in range(len):
        ans = max(ans, digit[i])
  
    print("Minimum Number of binary strings needed:", ans)
      
    # Traverse for all the binary strings
    for i in range(1, ans + 1, 1):
        num = 0
        for j in range(0, len, 1):
              
            # If digit at jth position is greater 
            # than 0 then substitute 1
            if (digit[j] > 0):
                num = num * 10 + 1
                digit[j] -= 1
            else:
                num *= 10
        print(num, end = " ")
  
# Driver code
if __name__ == '__main__':
    n = 564
      
    minBinary(n)
      
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# program to find the minimum number of 
// binary Strings to represent a number
using System;
  
class GFG 
{
  
    // Function to find the minimum number of
    // binary Strings to represent a number
    static void minBinary(int n)
    {
        int[] digit = new int[10];
        int len = 0;
  
        while (n > 0) 
        {
            digit[len++] = n % 10;
            n /= 10;
        }
  
        // Storing digits in correct order
        digit = reverse(digit, 0, len - 1);
  
        int ans = 0;
  
        // Find the maximum digit in the array
        for (int i = 0; i < len; i++) 
        {
            ans = Math.Max(ans, digit[i]);
        }
  
        Console.Write("Minimum Number of binary"
                " Strings needed: " + ans + "\n");
  
        // Traverse for all the binary Strings
        for (int i = 1; i <= ans; i++)
        {
            int num = 0;
            for (int j = 0; j < len; j++) 
            {
                // If digit at jth position is greater
                // than 0 then substitute 1
                if (digit[j] > 0) 
                {
                    num = num * 10 + 1;
                    digit[j]--;
                }
                else
                {
                    num *= 10;
                }
            }
            Console.Write(num + " ");
        }
    }
  
    static int[] reverse(int []str, 
                         int start, int end)
    {
  
        // Temporary variable to store character
        int temp;
        while (start <= end)
        {
            // Swapping the first and 
            // last character
            temp = str[start];
            str[start] = str[end];
            str[end] = temp;
            start++;
            end--;
        }
        return str;
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        int n = 564;
  
        minBinary(n);
    }
}
  
// This code is contributed by 29AjayKumar

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Output:

Minimum No of binary strings needed: 6
111 111 111 111 110 10 

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