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Minimum number of Binary strings to represent a Number

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  • Last Updated : 17 Nov, 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 <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;
}

Java




// 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

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 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

C#




// 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

Javascript




<script>
 
// Javascript 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
    function minBinary(n)
    {
        var digit = Array(10).fill(0);
        var len = 0;
 
        while (n > 0) {
            digit[len++] = n % 10;
            n = parseInt(n/10);
        }
 
        // Storing digits in correct order
        digit = reverse(digit, 0, len - 1);
 
        var ans = 0;
 
        // Find the maximum digit in the array
        for (i = 0; i < len; i++) {
            ans = Math.max(ans, digit[i]);
        }
 
        document.write("Minimum Number of binary"
        + " Strings needed: " + ans + "<br/>");
 
        // Traverse for all the binary Strings
        for (i = 1; i <= ans; i++)
        {
            var num = 0;
            for (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;
                }
            }
            document.write(num + " ");
        }
    }
 
    function reverse(str , start , end) {
 
        // Temporary variable to store character
        var 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
     
        var n = 564;
 
        minBinary(n);
 
// This code contributed by umadevi9616
 
</script>

Output:  

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

Time Complexity: O(N)

Auxiliary Space: O(1)
 


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