Intersect all possible combinations of list elements

Question

I have a list of vectors:

> l <- list(A=c("one", "two", "three", "four"), B=c("one", "two"), C=c("two", "four", "five", "six"), D=c("six", "seven"))

> l
$A
[1] "one"   "two"   "three" "four"

$B
[1] "one" "two"

$C
[1] "two"  "four" "five" "six"

$D
[1] "six"   "seven"

I would like to calculate the length of the overlap between all possible pairwise combinations of the list elements, i.e. (the format of the result doesn't matter):

AintB 2
AintC 2
AintD 0
BintC 1
BintD 0
CintD 1

---

I know combn(x, 2) can be used to get a matrix of all possible pairwise combinations in a vector and that length(intersect(a, b)) would give me the length of the overlap of two vectors, but I can't think of a way to put the two things together.

Any help is much appreciated! Thanks.

Answer 1

combn works with list structures as well, you just need a little unlist'ing of the result to use intersect...

# Get the combinations of names of list elements
nms <- combn( names(l) , 2 , FUN = paste0 , collapse = "" , simplify = FALSE )

# Make the combinations of list elements
ll <- combn( l , 2 , simplify = FALSE )

# Intersect the list elements
out <- lapply( ll , function(x) length( intersect( x[[1]] , x[[2]] ) ) )

# Output with names
setNames( out , nms )
#$AB
#[1] 2

#$AC
#[1] 2

#$AD
#[1] 0

#$BC
#[1] 1

#$BD
#[1] 0

#$CD
#[1] 1