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Represent a number as sum of minimum possible psuedobinary numbers

Given a number, you have to represent this number as sum of minimum number of possible psuedobinary numbers. A number is said to be psuedobinary number if its decimal number consists of only two digits (0 and 1). Example: 11,10,101 are all psuedobinary numbers.

Examples :-

Input : 44
Output : 11 11 11 11

Explanation : 44 can be represented as sum of 
minimum 4 psuedobinary numbers as 11+11+11+11  

Input : 31
Output : 11 10 10

Explanation : 31 can be represented as sum of
minimum 3 psuedobinary numbers as 11+10+10  



The idea to do this is to first observe carefully that we need to calculate minimum number of possible psuedobinary numbers. To do this we find a new number m such that if for a place in given number n, the digit is non-zero then the digit in that place in m is 1 otherwise zero. For example if n = 5102, then m will be 1101. Then we will print this number m and subtract m from n. We will keep repeating these steps until n is greater than zero.

C++

// C++ program to represent a given 
// number as sum of minimum possible
// psuedobinary numbers
#include<iostream>
using namespace std;
  
// function to represent a given 
// number as sum of minimum possible
// psuedobinary numbers
void psuedoBinary(int n)
{
    // Repeat below steps until n > 0
    while (n > 0)
    {                 
        // calculate m (A number that has same
        // number of digits as n, but has 1 in
        // place of non-zero digits 0 in place
        // of 0 digits)
        int temp = n, m = 0, p = 1;
        while (temp)
        {
            int rem = temp % 10;
            temp = temp / 10;
  
            if (rem != 0)
                m += p;
              
            p *= 10;
        }
          
        cout << m << " ";
  
        // subtract m from n
        n = n - m;
    }
}
  
// Driver code
int main()
{
    int n = 31;
  
    psuedoBinary(n);
  
    return 0;
}

Java

// Java program to represent a given
// number as sum of minimum possible
// psuedobinary numbers
  
import java.util.*;
import java.lang.*;
  
class GFG
{
    public static void psuedoBinary(int n)
    {
        // Repeat below steps until n > 0
        while (n != 0)
        {
            // calculate m (A number that has same
            // number of digits as n, but has 1 in
            // place of non-zero digits 0 in place
            // of 0 digits)
            int temp = n, m = 0, p = 1;
            while(temp != 0)
            {
                int rem = temp % 10;
                temp = temp / 10;
  
                if (rem != 0)
                    m += p;
  
                p *= 10;
            }
  
            System.out.print(m + " ");
              
            // subtract m from n
            n = n - m;
        }
        System.out.println(" ");
    }
  
// Driver code
public static void main(String[] args)
    {
        int n = 31;
        psuedoBinary(n);
    }
}
  
// This code is contributed by Mohit Gupta_OMG

Python3

# Python3 program to represent 
# a given number as sum of 
# minimum possible psuedobinary 
# numbers
  
# function to represent a 
# given number as sum of
# minimum possible
# psuedobinary numbers
def psuedoBinary(n):
      
    # Repeat below steps
    # until n > 0
    while (n > 0):
          
        # calculate m (A number 
        # that has same number 
        # of digits as n, but 
        # has 1 in place of non-zero 
        # digits 0 in place of 0 digits)
        temp = n;
        m = 0;
        p = 1;
        while (temp):
            rem = temp % 10;
            temp = int(temp / 10);
              
            if (rem != 0):
                m += p;
            p *= 10;
          
        print(m,end=" ");
          
        # subtract m from n
        n = n - m;
  
# Driver code
n = 31;
psuedoBinary(n);
  
# This code is contributed
# by mits.

/div>

C#

// C# program to represent a given
// number as sum of minimum possible
// psuedobinary numbers
  
using System;
  
class GFG
{
    public static void psuedoBinary(int n)
    {
        // Repeat below steps until n > 0
        while (n != 0)
        {
            // calculate m (A number that has same
            // number of digits as n, but has 1 in
            // place of non-zero digits 0 in place
            // of 0 digits)
            int temp = n, m = 0, p = 1;
            while(temp != 0)
            {
                int rem = temp % 10;
                temp = temp / 10;
  
                if (rem != 0)
                    m += p;
  
                p *= 10;
            }
  
            Console.Write(m + " ");
              
            // subtract m from n
            n = n - m;
        }
        Console.Write(" ");
    }
  
// Driver code
public static void Main()
    {
        int n = 31;
        psuedoBinary(n);
    }
}
  
// This code is contributed by nitin mittal

PHP

<?php
// PHP program to represent a 
// given number as sum of minimum 
// possible psuedobinary numbers
  
// Function to represent a 
// given number as sum of minimum 
// possible psuedobinary numbers
function psuedoBinary($n)
{
    // Repeat below steps until n > 0
    while ($n > 0)
    {                 
        // calculate m (A number 
        // that has same number of 
        // digits as n, but has 1 
        // in place of non-zero 
        // digits 0 in place of 0 
        // digits)
        $temp = $n; $m = 0; $p = 1;
        while ($temp)
        {
            $rem = $temp % 10;
            $temp = $temp / 10;
  
            if ($rem != 0)
                $m += $p;
              
            $p *= 10;
        }
          
        echo $m , " ";
  
        // subtract m from n
        $n = $n - $m;
    }
}
  
// Driver code
$n = 31;
psuedoBinary($n);
  
// This code is contributed
// by nitin mittal.
?>


Output :

11 10 10

Time Complexity : O( log n )
Auxiliary Space : O(1)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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