Related Articles

# Minimum number of Binary strings to represent a Number

• Last Updated : 03 May, 2021

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 substituting 0’s and 1’s greadily.

Below is the implementation of the above approach:

## C++

 // C++ program to find the minimum number of// binary strings to represent a number#include using namespace std; // Function to find the minimum number of// binary strings to represent a numbervoid 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 codeint main(){    int n = 564;         minBinary(n);         return 0;}

## Java

 // Java program to find the minimum number of// binary Strings to represent a numberimport 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

## Python3

 # 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 numberdef 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 codeif __name__ == '__main__':    n = 564         minBinary(n)     # This code is contributed by# Surendra_Gangwar

## C#

 // C# program to find the minimum number of// binary Strings to represent a numberusing 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

## Javascript



Output:

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

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up