Transforming a binary vector

In summary: You could also use a sorted list to do this. For example, if you have a list of three elements (T1,T2,T3), you could use the following code to get the sorted list:list.sort(function(a,b,c){return a-b+c});In summary, baxy is trying to figure out how to transform a set of binary vectors in such a way that the relation > is given by the fact that to convert B->A takes 1 step, C->A takes 2 steps, and C->B takes 1 step.
  • #1
baxy
2
0
Hi,

This is my first post and I must worn you that I'm not a mathematician. I am just a regular blonk looking for help concerning the following problem.

What i have is a set (T) of binary vectors:A: 100110
B: 000110
C: 010110now what i am trying to figure out is there a transformation, a function to transform given vectors in such a way that

A>B>C

where a relation > on T is given by the fact that to convert

B->A takes 1 step
C->A takes 2 steps
C->B takes 1 step

Can anyone suggest a book or a paper where such things are discussed , or give a few pointers?

Thank you,

baxy

PS

and the relation can ba symmetrical

A<B<C

as long as the order is preserved
 
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  • #2
Hey baxy and welcome to the forums.

I'm not exactly sure what you are trying to do, but it seems that you're given a set T = {T1,T2,T3} and you want to find a transformation that takes T1,T2,T3 in which f(T1) > f(T2) > f(T3) or f(T1) < f(T2) < f(T3).

One easy transformation that comes to mind if we assume that all entries of the set are non-zero is to use a transformation that maps an input vector to an output vector. In other words, using your set with three elements define F to be:

F(T1,T2,T3) = [T1+T2+T3,T2+T3,T3] where the output is a vector with three elements.

Since this is a linear transformation, you can create an appropriate matrix that represents this transformation and define that as your operator.

Is this what you had in mind?

Also I didn't take into account the binary nature of your number, so you would have to compensate for this in your computation.
 
  • #3
ok, but i didn't quite understand how can i from this output vector figure out that T1>T2>T3 ? so what i need t do is transform my vectors into something and then just by sorting the transforms, figure out that T1_{A} needs 1 transformation step to be converted to T2_{B} and 2 transformation step to be converted to T3_{C}.

This is my problem.
 
  • #4
baxy said:
ok, but i didn't quite understand how can i from this output vector figure out that T1>T2>T3 ? so what i need t do is transform my vectors into something and then just by sorting the transforms, figure out that T1_{A} needs 1 transformation step to be converted to T2_{B} and 2 transformation step to be converted to T3_{C}.

This is my problem.

Ohh I see what you mean.

Well to sort two elements the first one is min(T1,T2) and the last is max(T1,T2). Can you adapt this for three elements?
 
  • #5

Hello baxy,

Thank you for reaching out with your question. I am happy to assist you in finding a solution to your problem.

From what I understand, you are looking for a transformation or function that can convert a set of binary vectors (A, B, C) into a specific order, where A is greater than B and C, and B is greater than C. This can also be expressed as A > B > C, with the caveat that the order must be preserved.

I would recommend looking into the field of combinatorics, specifically the study of permutations and combinations. This field deals with the arrangement and transformation of objects in a specific order. In your case, the objects are the binary vectors and the desired order is A > B > C.

You may also want to explore the concept of Hamming distance, which is used to measure the number of differences between two binary vectors. This could be helpful in determining the number of steps needed to transform one vector into another.

I am not aware of a specific book or paper that discusses this exact problem, but I suggest looking into textbooks or research papers on combinatorics, or reaching out to a mathematician or computer scientist who specializes in this area.

I hope this helps guide you in finding a solution to your problem. Good luck!

Best,
 

What is a binary vector?

A binary vector is a data structure that represents a sequence of 0s and 1s. It is commonly used in computer science and mathematics to represent and manipulate binary data.

How do you transform a binary vector?

To transform a binary vector, you can use various operations such as bitwise AND, OR, XOR, and NOT. These operations allow you to manipulate the individual bits in the vector and create new vectors with different patterns of 0s and 1s.

What is the purpose of transforming a binary vector?

The purpose of transforming a binary vector is to perform logical operations and create new vectors with specific patterns. This can be useful in data processing, coding, and other applications where binary data is involved.

Can a binary vector be transformed into different types of data?

Yes, a binary vector can be transformed into other types of data by converting it into a different base, such as decimal or hexadecimal. It can also be used to represent other types of data, such as characters, images, and audio.

Are there any limitations to transforming a binary vector?

There are some limitations to transforming a binary vector. For example, the length of the vector must be a multiple of the number of bits in a byte. Additionally, some logical operations may result in an overflow or underflow, depending on the number of bits in the vector.

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