Minimum number of Binary strings to represent a Number

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++
Java
Python3
C#
Javascript
// 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 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 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 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# 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
<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) 
SURENDRA_GANGWAR
29AjayKumar
umadevi9616
rohitsingh07052
binary-string
Greedy Algorithms
Arrays
Greedy
Arrays
Greedy
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