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Represent a Number as Sum of Minimum Possible Pseudo-Binary Numbers in C++
This tutorial will discuss the representation of a number as a sum of minimum pseudo-binary numbers. Pseudo-binary numbers are the numbers that consist of only binary digits, i.e., 0 and 1. Examples of pseudo-binary numbers are 00, 11, 10, 100, 111, 1011, etc.
Below are some examples of numbers represented as the sum 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
Approach to Find the Solution
Below is one of the best approaches to find minimum pseudo-binary numbers to represent N.
Take a number X and update its digits to 1 or 0 according to the digits of the number N.
Check digit at each place of N,
If it is 0, then update that place of X to 0.
If it is not zero, update that place of X to 1.
Let’s say N = 32, then X will be 11
Then X will be one pseudo-binary number.
Now decrement N by X and repeat step1 until N becomes zero.
Example
C++ Code for the Above Approach
#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's and 1'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 for taking N and picking digits on every place to find X.
We are updating the value of the temp variable with N and Inner loop for checking each place of temp variable and updating that place of variable X.
Printing value of X because that is one pseudo-binary number.
We update N by subtracting with X and going to the outer loop again until N becomes 0.
Conclusion
In this tutorial, we have discussed how we can represent a number as a sum of minimum possible pseudo-binary numbers. We discussed the approach to find all the pseudo-binary numbers. We also discussed the C++ code for the same, which we can write in any other programming language like C, Java, Python, etc. We hope you find this tutorial helpful.
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