C ++: efficient way to check if elements in a vector are greater than elements in another that have the same indices?

I have it vector < vector <int> >

like this:

v = {{1,2,3}, {4,2,1}, {3,1,1}....}}

      

        
        
        
      

    

All the elements v

, such as v[0]

, v[1]

, v[2]

... are the same size. There may be duplicate items.

I am trying to find and remove vectors (for example v[2]

) that are "majorized" by another vector (for example v[1]

), i.e. all elements v[1]

greater than / equal to the corresponding elements (in index order) in v[2]

.

A naive way to do this would be to walk through v

and compare each vector to another vector, and additionally compare each element to another vector element.

But I believe the best way to do this is without getting O(n^3)

all the vectors in the element count v

.

If multiple vectors are equal, I only need one of them (i.e. remove all but one). A random selection would be enough.

Any thoughts or ideas are appreciated!