Concatenate/paste strings of varying length according to index - r

Question

I would like to know how to concatenate string to form sequences of different and varying lengths & varying content according to one condition.
Here is a dataframe example (my DF is actually about 60000 rows).
column index: just an index
to_concat: the string item i want to concatenate
max_seq: one example of the condition for concatenation (to_concat should only concatenate if it is part of the same sequence - and I have indicated the position of the string in the sequence for now.
concat_result: The result I would like to have
index to_concat max_seq concat_result
1 Abc! 1 <abc!+def+_>
2 def 2 <abc!+def+_>
3 _ 3 <abc!+def+_>
4 x93 1 <x93+afza+5609+5609+Abc!+def>
5 afza 2 <x93+afza+5609+5609+Abc!+def>
6 5609 3 <x93+afza+5609+5609+Abc!+def>
7 5609 4 <x93+afza+5609+5609+Abc!+def>
8 Abc! 5 <x93+afza+5609+5609+Abc!+def>
9 def 6 <x93+afza+5609+5609+Abc!+def>
10 _ 1 <_+x93+afza>
11 x93 2 <_+x93+afza>
12 afza 3 <_+x93+afza>
I know of paste & aggregate, length, probably usefull.. But do not see in which order to do that and especially how to formulate the paste.
I suppose I should also include an "second" index better done for max_seq (such as : all strings to be concatenated in the same sequence have the same number so here we would have a 3 sequences " 1 1 1 2 2 2 2 2 2 3 3 3 ".
But I do not know if that is the quickest/easiest solution and also I do not know how to paste varying length...
Could you please help a fellow PhD? Thanks a lot in advance.
Reproductible example:
dput(dat)
> dput(dat)
structure(list(V1 = c("index", "1", "2", "3", "4", "5", "6",
"7", "8", "9", "10", "11", "12"), V2 = c("to_concat", "Abc!",
"def", "_", "x93", "afza", "5609", "5609", "Abc!", "def", "_",
"x93", "afza"), V3 = c("max_seq", "1", "2", "3", "1", "2", "3",
"4", "5", "6", "1", "2", "3"), V4 = c("concat_result", "<abc!+def+_>",
"<abc!+def+_>", "<abc!+def+_>", "<x93+afza+5609+5609+Abc!+def>",
"<x93+afza+5609+5609+Abc!+def>", "<x93+afza+5609+5609+Abc!+def>",
"<x93+afza+5609+5609+Abc!+def>", "<x93+afza+5609+5609+Abc!+def>",
"<x93+afza+5609+5609+Abc!+def>", "<_+x93+afza>", "<_+x93+afza>",
"<_+x93+afza>")), .Names = c("V1", "V2", "V3", "V4"), class = "data.frame", row.names = c(NA,
-13L))

Answer 1

Several options to get the desired result:
1) Using base R:
mydf$grp <- cumsum(mydf$max_seq < c(1,head(mydf$max_seq, -1))) + 1
mydf$concat_result <- ave(mydf$to_concat, mydf$grp,
FUN = function(x) paste0('<',paste(x,collapse='+'),'>'))
which gives:
> mydf
index to_concat max_seq grp concat_result
1 1 Abc! 1 1 <Abc!+def+_>
2 2 def 2 1 <Abc!+def+_>
3 3 _ 3 1 <Abc!+def+_>
4 4 x93 1 2 <x93+afza+5609+5609+Abc!+def>
5 5 afza 2 2 <x93+afza+5609+5609+Abc!+def>
6 6 5609 3 2 <x93+afza+5609+5609+Abc!+def>
7 7 5609 4 2 <x93+afza+5609+5609+Abc!+def>
8 8 Abc! 5 2 <x93+afza+5609+5609+Abc!+def>
9 9 def 6 2 <x93+afza+5609+5609+Abc!+def>
10 10 _ 1 3 <_+x93+afza>
11 11 x93 2 3 <_+x93+afza>
12 12 afza 3 3 <_+x93+afza>
2) Or using the data.table package:
library(data.table)
setDT(mydf)[, grp := cumsum(max_seq < shift(max_seq, fill = 0))+1
][, concat_result := paste0('<',paste(to_concat,collapse='+'),'>'), grp][]
3) Or using the dplyr package:
library(dplyr)
mydf %>%
mutate(grp = cumsum(max_seq < lag(max_seq, n=1, default=0))+1) %>%
group_by(grp) %>%
mutate(concat_result = paste0('<',paste(to_concat,collapse='+'),'>'))
Used data:
mydf <- structure(list(index = 1:12,
to_concat = c("Abc!", "def", "_", "x93", "afza", "5609", "5609", "Abc!", "def", "_", "x93", "afza"),
max_seq = c(1L, 2L, 3L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L)),
.Names = c("index", "to_concat", "max_seq"), class = "data.frame", row.names = c(NA, -12L))