I have asked this question previously (see here) and received a satisfactory answer using the purr
package. However, this has proved to be a bottle neck in my program so I would like to rewrite the section using the RCPP
package.
Proper subset : A proper subset S' of a set S is a subset that is strictly contained in S and so excludes S itself (note I am also excluding the empty set).
Suppose you have the following vectors in a list:
a = c(1,2)
b = c(1,3)
c = c(2,4)
d = c(1,2,3,4)
e = c(2,4,5)
f = c(1,2,3)
My aim is to keep only vectors which have no proper subset within the list, which in this example would be a, b and c.
Previous Solution
library(purr)
possibilities <- list(a,b,c,d,e,f)
keep(possibilities,
map2_lgl(.x = possibilities,
.y = seq_along(possibilities),
~ !any(map_lgl(possibilities[-.y], function(z) all(z %in% .x)))))
The notion here is to avoid the O(N^3) and use a less order instead. The other answer provided here will be slow still since it is greater than O(N^2). Here is a solution with less than O(N^2), where the worst case scenario is O(N^2) when all the elements are unique.
onlySet <- function(x){
i <- 1
repeat{
y <- sapply(x[-1], function(el)!all(is.element(x[[1]], el)))
if(all(y)){
if(i==length(x)) break
else i <- i+1
}
x <- c(x[-1][y], x[1])
}
x
}
Now to show the time difference, check out the following:
match_fun <- Vectorize(function(s1, s2) all(s1 %in% s2))
method1 <- function(a){
mat <- outer(a, a, match_fun)
a[colSums(mat) == 1]
}
poss <- rep(possibilities, 100)
microbenchmark::microbenchmark(method1(poss), onlySet(poss))
Unit: milliseconds
expr min lq mean median uq max neval cld
method1(poss) 840.7919 880.12635 932.255030 889.36380 923.32555 1420.1077 100 b
onlySet(poss) 1.9845 2.07005 2.191647 2.15945 2.24245 3.3656 100 a
Have you tried optimising the solution in base R first? For example, the following reproduces your expected output and uses (faster) base R array routines:
match_fun <- Vectorize(function(s1, s2) all(s1 %in% s2))
mat <- outer(possibilities, possibilities, match_fun)
possibilities[colSums(mat) == 1]
#[[1]]
#[1] 1 2
#
#[[2]]
#[1] 1 3
#
#[[3]]
#[1] 2 4
Inspired by Onyambu's performant solution, here is another base R option using a recursive function
f_recursive <- function(x, i = 1) {
if (i > length(x)) return(x)
idx <- which(sapply(x[-i], function(el) all(x[[i]] %in% el))) + 1
if (length(idx) == 0) f_recursive(x, i + 1) else f_recursive(x[-idx], i + 1)
}
f(possibilities)
The performance is on par with Onyambu's solution.
poss <- rep(possibilities, 100)
microbenchmark::microbenchmark(
method1(poss),
onlySet(poss),
f_recursive(poss))
#Unit: milliseconds
# expr min lq mean median uq
# method1(poss) 682.558602 710.974831 750.325377 730.627996 765.040976
# onlySet(poss) 1.700646 1.782713 1.870972 1.819820 1.918669
# f_recursive(poss) 1.681120 1.737459 1.884685 1.806384 1.901582
# max neval
# 1200.562889 100
# 2.371646 100
# 3.217013 100
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