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r - Split comma-separated strings into boolean columns

I have:

id choice
----------
1  "a,b,c"
2  "c"
3  "a,c"
4  "b,c"

I need

id a b c
---------
1  1 1 1
2  0 0 1
3  0 0 1
4  0 1 1

(or equivalent with TRUE/FALSE values)

Is there any way to do this in R? I've looked into strsplit but that doesn't seem to help.

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This is exactly what cSplit_e from my "splitstackshape" package is designed to do.

library(splitstackshape)
cSplit_e(DF, "choice", sep = ",", mode = "binary", 
         type = "character", fill = 0, drop = TRUE)
#   id choice_a choice_b choice_c
# 1  1        1        1        1
# 2  2        0        0        1
# 3  3        1        0        1
# 4  4        0        1        1

This uses DF from @G.Grothendieck's answer as the input:

Lines <- 'id choice
----------
1  "a,b,c"
2  "c"
3  "a,c"
4  "b,c"'
DF <- read.table(text = Lines, header = TRUE, comment = "-", as.is = TRUE)

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