In C++, represent a number as the smallest possible sum of pseudo-binary numbers

This tutorial will discuss representing a number as the smallest sum of pseudo-binary numbers. A pseudo-binary number is a number composed of the binary digits 0 and 1. Examples of pseudo-binary numbers are 00, 11, 10, 100, 111, 1011, etc.

Here are some examples of numbers represented as sums of pseudo-binary numbers.

Input : 23
Output : 11 + 11 + 1
Explanation : 23 = 11 + 11 + 1, sum of pseudo-binary numbers(11, 11, 1) is 23.

Input : 50
Output : 10 + 10 + 10 + 10 + 10

Methods to find the solution

The following is one of the best ways to find the smallest pseudo-binary number that represents N.

• Take a number X and update the number of digits in X to 1 or 0 according to each digit of the number N.

• Check each digit of N:

  • If it is 0, set that bit of X to 0.

  • If it is not 0, set the bit of X to 1.

  • Assuming N = 32, X will become 11.

• # Then X will become a pseudo-binary number.

• Now subtract X from N and repeat step 1 until N becomes zero.

Example

C code for the above method

#include<iostream>
using namespace std;
int main(){
   int N = 51;
   // find a pseudo-binary number until N becomes 0.
   cout << "pseudo-binary representation of " << N << " is: ";
   while (N > 0){                
      // finding X which contains 0&#39;s and 1&#39;s according to N.
      int temp = N;
      int X = 0, bit = 1;
      // checking each place of N for zero or non-zero.
      while (temp!=0){
      int last_dig = temp % 10;
      temp = temp / 10;
      if (last_dig != 0)
         X += bit;
         bit *= 10;
      }
      // printing one pseudo-binary number.
      cout << X << " ";
      // Updating N by subtracting with X.
      N = N - X;
       
   }
   return 0;
}

Output

pseudo-binary representation of 51 is: 11 10 10 10 10

Understanding the code

• An outer while loop is used to get N and select the number at each position to find X.

• We do this by updating the value of N into the temp variable and using an inner loop to check each position of the temp variable and update that position of the variable X.

• Print the value of X because it is a pseudo-binary number.

• We update N by subtracting X from N and entering the outer loop again until N becomes 0.

Conclusion

In this tutorial, we discussed how to represent a number as the smallest possible sum of pseudo-binary numbers. We discussed ways to find all pseudo-binary numbers. We also discussed that the same C code we can write in other programming languages ​​like C, Java, Python, etc. Hope you find this tutorial helpful.

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