Return All Possible Combinations of Values

Question

I have the following table:

Group Value
----  ----
1     A
1     B
1     C
1     D
2     A
2     B
2     C

For each of the two groups, I want to return all possible combinations of values. For group 1, e.g., the possible combinations of are (A,B), (A,C), (A,D), (B,C), (B,D), (C,D), (A,B,C), (B,D,C), (D,C,A), (C,A,B). Analogous, for group 2 it is (A,B), (A,C), (B,C) [Remark: I don't want to consider (1) the combintions with just one value, (2) the combination with all values and (3) the combination with no values. Thus I have 2^(n)-n-1-1 combinations for n different values].

I want to list all those combinations with the help of an additional column "Combi". This column numbers the different combinations consecutively.

Group Combi Value
----  ----  ----
1     1     A
1     1     B
1     2     A
1     2     C
1     3     A
1     3     D
1     4     B
1     4     C
1     5     B
1     5     D
1     6     C
1     6     C
1     7     A
1     7     B
1     7     C
1     8     B
1     8     C
1     8     D
1     9     C
1     9     D
1     9     A
1     10    D
1     10    A
1     10    B
2     11    A
2     11    B
2     12    A
2     12    C
2     13    B
2     13    C

How do I do this in R?

Answer 1

Here is a general tidyverse solution, should work with sets of values that have more than 3 items.

The idea is to use combn (with m = 2 then 3 etc) and format the output as a tibblefor different Group and m values. From there we can use tidyverse functions map_dfr and unnest. Finally as we have multiple ids rather than one, we build a table of unique ids, build the unique combi id and join it back to our result.

# convenience fonction to store combinations in a long format
combi_as_tibble <- function(n,values) combn(values,n) %>%
  {tibble(id = rep(seq(ncol(.)),each=nrow(.)),Value=c(.))}    
combi_as_tibble(2,letters[1:3]) # example
# # A tibble: 6 x 2
#      id Value
#   <chr> <chr>
# 1     1     a
# 2     1     b
# 3     2     a
# 4     2     c
# 5     3     b
# 6     3     c


df1 %>% group_by(Group) %>%
  summarize(combis = list(
    map_dfr(2:(length(unique(Value))-1),combi_as_tibble,Value,.id="id2")
  ))     %>% # by Group, build a long tibble with all combinations
  unnest %>% # unnest to get a long unnested table
  left_join(.,select(.,Group,id2,id) %>% distinct %>% mutate(combi=row_number())
  )      %>% # build combi ids
  select(Group,Value,combi) %>%
  as.data.frame

#    Group Value combi
# 1      1     A     1
# 2      1     B     1
# 3      1     A     2
# 4      1     C     2
# 5      1     A     3
# 6      1     D     3
# 7      1     B     4
# 8      1     C     4
# 9      1     B     5
# 10     1     D     5
# 11     1     C     6
# 12     1     D     6
# 13     1     A     7
# 14     1     B     7
# 15     1     C     7
# 16     1     A     8
# 17     1     B     8
# 18     1     D     8
# 19     1     A     9
# 20     1     C     9
# 21     1     D     9
# 22     1     B    10
# 23     1     C    10
# 24     1     D    10
# 25     2     A    11
# 26     2     B    11
# 27     2     A    12
# 28     2     C    12
# 29     2     B    13
# 30     2     C    13

data

df1 <- read.table(text="Group Value
1     A
1     B
1     C
1     D
2     A
2     B
2     C",h=T,strin=F)