Minimum number of Binary strings to represent a Number

Last Updated : 16 Nov, 2022

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 greedily.

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# 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)

Binary representation of a given number

md1844

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Minimum number of Binary strings to represent a Number

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