Getting unique, non-redundant combinations in Julia array?

Question

I have two arrays of variables I am comparing,

arr1 = [1,2,3]
arr2 = [1,2,3]

I would like to get each unique, non-redundant combination of variables. The initial unique combinations are:

(1,1), (1,2), (1,3)
(2,1), (2,2), (2,3)
(3,1), (3,2), (3,3)

But this set is further reduced, since comparing variable 1 with itself (and 2 with itself, etc.) is meaningless. Removing these, the set reduces to:

(1,2), (1,3)
(2,1), (2,3)
(3,1), (3,2)

Furthermore, there are redundant pairs since comparing variable 1 to variable 2 is the same as comparing variable 2 to variable 1. So the end result I'm looking for would be:

(1,2), (1,3), (2,3)

I can reason through the first bit:

# Generate combination arrays
sets = []
sy = 3
for i in 1:size(ellipseX)[2]
    set1 = repeat([i],sy)
    set2 = range(1,sy)
    newsets = cat(set1,set2,dims=2)
    sets = cat(sets,newsets,dims=1)
end
# Remove rows with same column values
for N in 0:sy-1
    rownum = 1+sy*N
    sets = sets[setdiff(1:end, rownum), :]
end

but removing the redundant pairs is a bit more tricky. Is there a much easier way to do this?

Answer 1

This seems like a job for Combinatorics.jl.

using Combinatorics

arr1 = [1,2,3]
arr2 = [1,2,3]

arr = unique([arr1; arr2])
combs = combinations(arr,2) |> collect
 [1, 2]
 [1, 3]
 [2, 3]

If, for some reason you can't install Combinatorics.jl, a comprehension will also work.

n = length(arr)
combs = [(arr[i],arr[j]) for i = 1:n-1 for j = i+1:n]
(1, 2)
(1, 3)
(2, 3)

Update: If the arrays might have different numbers, another in-place filtering operation is required to make sure the output tuples have one element taken from arr1 and the other element taken from arr2.

filter!(t->any(t .∈ (arr1,)) && any(t .∈ (arr2,)), combs)

Example:

arr1 = [1,2,3,4]
arr2 = [1,2,5]

U = unique([arr1; arr2])

n = length(U)
combs = [(U[i],U[j]) for i=1:n-1 for j=i+1:n]
filter!(t->any(t .∈ (arr1,)) && any(t .∈ (arr2,)), combs)
9-element Vector{Tuple{Int64, Int64}}:
 (1, 2)
 (1, 3)
 (1, 4)
 (1, 5)
 (2, 3)
 (2, 4)
 (2, 5)
 (3, 5)
 (4, 5)