Find all numbers in range with local min and global max - r

Question

I have a dataframe testData which is made up of many unique ids. My objective is to identify whether or not the ids contain all of the possible integers in the range of month, yday, and week where the min is the first value per id and max is the max value in the entire range of the column
Please note this is different from the related question here
In other words, if id has all possible values in the range in month, then it should receive a t. For example, under month where id = 1, the min value is 2 and the max value for the whole column is 5, therefore 1 should receive a true because there is a value 2, 3, 4, and 5. Where id = 2, however, there are only values 1, 2, 4, and 5, so the 3 was skipped and therefore 2 should receive an f.
So far, I have a formula that takes all the values in the entire range of the column (but NOT the min value per id):
library(data.table)
setDT(testData)
output<-testData[,.(month=all(unique(testData$month)%in%.SD$month),yday=all(unique(testData$yday)%in%.SD$yday),week=all(unique(testData$week)%in%.SD$week)),by=(id)]
Any idea how I could integrate min where min is the minimum value per id and max is the maximum value in the range?
> testData
id month yday week
1 1 2 1 1
2 3 1 2 1
3 4 1 3 1
4 2 1 4 1
5 3 3 5 2
6 4 3 6 3
7 2 2 7 1
8 3 1 8 3
9 1 2 9 2
10 5 4 10 3
11 3 2 11 1
12 4 4 12 1
13 5 4 13 2
14 1 3 14 3
15 1 4 15 1
16 1 5 16 2
17 2 4 17 3
18 2 5 18 1
19 5 5 19 1
> dput(testData)
structure(list(id = c(1L, 3L, 4L, 2L, 3L, 4L, 2L, 3L, 1L, 5L,
3L, 4L, 5L, 1L, 1L, 1L, 2L, 2L, 5L), month = c(2L, 1L, 1L, 1L,
3L, 3L, 2L, 1L, 2L, 4L, 2L, 4L, 4L, 3L, 4L, 5L, 4L, 5L, 5L),
yday = 1:19, week = c(1L, 1L, 1L, 1L, 2L, 3L, 1L, 3L, 2L,
3L, 1L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 1L)), .Names = c("id",
"month", "yday", "week"), class = "data.frame", row.names = c(NA,
-19L))
In the end, the output should look like this:
> output
id month yday week
1 1 t f t
2 2 f f f
3 3 f f t
4 4 f f f
5 5 t f t

Answer 1

Using dplyr you can group by id and then just check whether all elements of the range are in the values present for each group. Note that min(month) gives the min for the grouped id variable, but max(testData$month) gives the max for the whole list.
library(dplyr)
tD2 <- testData %>% group_by(id) %>%
summarise(month=all(min(month):max(testData$month) %in% month),
yday=all(min(yday):max(testData$yday) %in% yday),
week=all(min(week):max(testData$week) %in% week))
tD2
# A tibble: 5 × 4
id month yday week
<int> <lgl> <lgl> <lgl>
1 1 TRUE FALSE TRUE
2 2 FALSE FALSE FALSE
3 3 FALSE FALSE TRUE
4 4 FALSE FALSE FALSE
5 5 TRUE FALSE TRUE