A more general function for the number of matching elements among the n elements of a list

Question

I am trying to calculate the number of common entries among the elements of a list:

temp<-list(element1=c("a","b","c"), element2=c("b","c","d"), 
           element3=c("d","e","f"), element4=c("a","c","z"))

To get the overlap among all pairwise combinations of the elements, this function works:

calculate.overlap.2<-function(y){
  pw<-combn(y,2,FUN=function(x)sum(x[[1]]%in%x[[2]]))
  names(pw)<-combn(y,2,FUN=function(x)paste(names(x)[[1]],names(x)[[2]],sep="-"))
  return(pw)
}

To get the overlap among all three-way combinations of the elements, this function works:

calculate.overlap.3<-function(y){
   pw<-combn(y,3,FUN=function(x)sum(x[[1]]%in%x[[2]]&x[[1]]%in%x[[3]]))
   names(pw)<-combn(y,3,FUN=function(x) paste(names(x)[[1]],names(x)[[2]],names(x)[[3]],sep="-"))
   return(pw)
}

but as you can tell from the numbers inside the function, this is not an elegant solution.

It would be really nice to generalize these two functions into one, and have a function takes as an input the elements in each check of overlap. That is, an input of number.of.elements.per.comparison=2 would be equivalent to calculate.overlap.2 above and an input to the function of number.of.elements.per.comparison=3 would be the same as calculate.overlap.3.

I feel like there is a very elegant solution to this, but I just can't see it.

Answer 1

calculate.overlap <- function(y, i){
  pw <- combn(seq_along(y), i, FUN= function(x) {
    res <- length(Reduce(intersect, y[x]))
    names(res) <- paste(names(y[x]), collapse = "-")
    res
  }, simplify = FALSE)
  do.call(c, pw)
}

calculate.overlap(temp, 3)
#element1-element2-element3 element1-element2-element4 element1-element3-element4 element2-element3-element4 
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