问题
I have to sets A={1,2,3} and B={a,b,c,d,e}. I want the set of subsets of elements from both A and B that contain at least one element of A and one element of B. As clearified here: Cartesian product with all elements, I need to use the following formula:
P(A ∪ B)∖(P(A) ∪ P(B))
In R, I tried the following query:
require(HapEstXXR)
A <- c(1,2,3)
B <- c("A", "B", "C", "D", "E")
setdiff(powerset(union(A,B)), union(powerset(A),powerset(B)))
As as result I got 221 elements. As far as I know, there should be (2^3-1)(2^5-1) = 217 elements.
Is my query wrong?
回答1:
length( s1 <- powerset(union(A,B)) ) #255
length( s2 <- union(powerset(A),powerset(B)) ) # 38
255-38 = 217, which seems to be what you are looking for
However, not all of s2 are contained in s1
setdiff(s2, s1)
# 8 sets to create.
# 32 sets to create.
# 256 sets to create.
# [[1]]
# [1] 1 2
#
# [[2]]
# [1] 1 3
#
# [[3]]
# [1] 2 3
#
# [[4]]
# [1] 1 2 3
These 4 elements explain the difference beween 221 and 217
回答2:
Don't mix classes:
length( z <- setdiff(powerset(union(A,B)), union(powerset(as.character(A)),powerset(B))) )
# 217
Notice that as.character is applied to A.
来源：https://stackoverflow.com/questions/31185513/calculating-powerset-in-r