Skip to content
Related Articles

Related Articles

Minimum Deci-Binary numbers required to obtain a given sum S
  • Difficulty Level : Basic
  • Last Updated : 23 Dec, 2020

Given a numeric string S representing a positive decimal integer, the task is to find the minimum number of positive Deci-Binary numbers required to obtain the sum S.

Deci-Binary Numbers: Decimal numbers consisting of only 0s and 1s as its digits. 
 

Examples:

Input: S = “31”
Output: 3
Explanation: S can be represented as the sum of minimum of 3 Deci-Binary numbers {10, 10, 11}.

Input: S = “82734”
Output: 8
Explanation: S can be represented as sum minimum of 8 Deci-Binary numbers {11111, 11111, 10111, 10101, 10100, 10100, 10100, 10000}.



Approach: The given problem can be solved based on the following observations: 

Suppose X Deci-Binary numbers are needed to obtain the sum S. To make the sum of X Deci-Binary numbers at i-th place equal to a digit d in S, there must be exactly d Deci-Binary numbers among X numbers having 1 at the ith position. 
Therefore, the minimum number of Deci-Binary numbers required to obtain a sum S is equal to the maximum value of any of the digits of S.

Therefore, to solve the problem, iterate over the characters of the string S and find the maximum digit present in it.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ Program to implemeent
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the count of minimum
// Deci-Binary numbers required to obtain S
int minimum_deci_binary_number(string s)
{
    // Stores the minimum count
    int m = INT_MIN;
 
    // Iterate over the string s
    for (int i = 0; i < s.size(); i++) {
 
        // Convert the char to its
        // equivalent integer
        int temp = s[i] - '0';
 
        // If current character is
        // the maximum so far
        if (temp > m) {
 
            // Update the maximum digit
            m = temp;
        }
    }
 
    // Print the required result
    return m;
}
 
// Driver Code
int main()
{
 
    string S = "31";
    cout << minimum_deci_binary_number(S);
 
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to implemeent
// the above approach
class GFG{
     
// Function to find the count of minimum
// Deci-Binary numbers required to obtain S
static int minimum_deci_binary_number(String s)
{
     
    // Stores the minimum count
    int m = Integer.MIN_VALUE;
 
    // Iterate over the string s
    for(int i = 0; i < s.length(); i++)
    {
         
        // Convert the char to its
        // equivalent integer
        int temp = s.charAt(i) - '0';
 
        // If current character is
        // the maximum so far
        if (temp > m)
        {
             
            // Update the maximum digit
            m = temp;
        }
    }
     
    // Print the required result
    return m;
}
 
// Driver Code
public static void main (String[] args)
{
    String S = "31";
     
    System.out.println(minimum_deci_binary_number(S));
}
}
 
// This code is contributed by AnkThon

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 Program to implemeent
# the above approach
 
# Function to find the count of minimum
# Deci-Binary numbers required to obtain S
def minimum_deci_binary_number(s):
     
    # Stores the minimum count
    m = -10**19
 
    # Iterate over the string s
    for i in range(len(s)):
 
        # Convert the char to its
        # equivalent integer
        temp = ord(s[i]) - ord('0')
 
        # If current character is
        # the maximum so far
        if (temp > m):
 
            # Update the maximum digit
            m = temp
 
    # Prthe required result
    return m
 
# Driver Code
if __name__ == '__main__':
 
    S = "31"
    print(minimum_deci_binary_number(S))
 
# This code is contributed by mohit kumar 29

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to implemeent
// the above approach
using System;
class GFG
{
     
    // Function to find the count of minimum
    // Deci-Binary numbers required to obtain S
    static int minimum_deci_binary_number(string s)
    {
         
        // Stores the minimum count
        int m = int.MinValue;
     
        // Iterate over the string s
        for(int i = 0; i < s.Length; i++)
        {
             
            // Convert the char to its
            // equivalent integer
            int temp = s[i] - '0';
     
            // If current character is
            // the maximum so far
            if (temp > m)
            {
                 
                // Update the maximum digit
                m = temp;
            }
        }
         
        // Print the required result
        return m;
    }
     
    // Driver Code
    public static void Main (String[] args)
    {
        string S = "31";       
        Console.WriteLine(minimum_deci_binary_number(S));
    }
}
 
// This code is contributed by AnkThon

chevron_right


Output: 

3

 

Time Complexity: O(N)
Auxiliary Space: O(N)

 

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.

My Personal Notes arrow_drop_up
Recommended Articles
Page :