identified distinct arrangement of values by groups in data.frame - r

Question

I have a large dataframe that has as it's primary organization a single row with groups that are all identical length (in the toy example 3).
df <- data.frame(groups = c("gr1","gr1","gr1","gr2","gr2","gr2","gr3","gr3","gr3"),
no = c(1, 2, 3, 1, 2, 3, 1, 2, 3),
colA = c("a", "b", "c", "a", "b", "c", "a", "b", "c"),
colB = c("a", "b", "c", "X_", "b", "c", "a", "b", "c"),
colC = c("a", "b", "c", "X_", "b", "c", "c", "b", "a"))
df
> df
> groups no colA colB colC
> 1 gr1 1 a a a
> 2 gr1 2 b b b
> 3 gr1 3 c c c
> 4 gr2 1 a X_ X_
> 5 gr2 2 b b b
> 6 gr2 3 c c c
> 7 gr3 1 a a c
> 8 gr3 2 b b b
> 9 gr3 3 c c a
I want to identify for each column which group is the first example of a unique arrangement of values. So for colA it should return (T, F, F) since all three groups are identical so only group one is the 1st unique on. For colB it should return (T, T, F) since there are two distinct groups and only the 3rd is identical to the 1st. And for colC it should be (T, T, T) since the order of items matters.
So the final output could be a matrix like this
colA colB colC
> gr1 T T T
> gr2 F T T
> gr3 F F T
I think I could figure this out by breaking down the data frame into pairs of group and colA/B/B, identify which ones are identical, storing the results in a vector, and then reassembling the whole deal. But I am seeing a ton of for-loops and have a hard time thinking about how to vectorize this. I have been using dplyr a bit, but I don't yet see how it can help.
Maybe there's a decent way to unstack each of the columns based on the groups and then run a comparison across the relevant subsets of new (and shorter) columns?
Edited to add:
Maybe group_by %>% summarize is a way to get at this. If the summary can essentially concatenate all values in a group per column into a really long string I could then see which of those is distinct per group?
Second edit:
I got as far as:
d1 <- df %>% group_by(groups) %>% summarise(colB = paste(unique(colB), collapse = ', ')) %>% distinct(colB)
which puts out
> # A tibble: 2 x 1
> colB
> <chr>
> 1 a, b, c
> 2 X_, b, c
It identifies the distinct groups, but I now have to figure out how to compare it against the rest full column to get T/F for each group.

Answer 1

Here's a base R approach :
cols <- grep('col', names(df))
cbind(unique(df[1]), sapply(df[cols], function(x)
!duplicated(by(x, df$groups, paste0, collapse = '-'))))
# groups colA colB colC
#1 gr1 TRUE TRUE TRUE
#4 gr2 FALSE TRUE TRUE
#7 gr3 FALSE FALSE TRUE

Answer 2

Your summarize idea is spot on:
df %>%
group_by(groups) %>%
summarize(across(starts_with("col"), paste, collapse = ""), .groups = "drop") %>%
mutate(across(starts_with("col"), ~!duplicated(.)))
# # A tibble: 3 x 4
# groups colA colB colC
# <chr> <lgl> <lgl> <lgl>
# 1 gr1 TRUE TRUE TRUE
# 2 gr2 FALSE TRUE TRUE
# 3 gr3 FALSE FALSE TRUE

Answer 3

With "data.table" you can try:
library(data.table)
cols <- c("colA", "colB", "colC")
fun <- function(x) !duplicated(x)
as.data.table(df)[, lapply(.SD, toString), groups, .SDcols = cols][
, (cols) := lapply(.SD, fun), .SDcols = cols][]
# groups colA colB colC
# 1: gr1 TRUE TRUE TRUE
# 2: gr2 FALSE TRUE TRUE
# 3: gr3 FALSE FALSE TRUE