# How to flatten a list to a list without coercion?

I am trying to achieve the functionality similar to unlist, with the exception that types are not coerced to a vector, but the list with preserved types is returned instead. For instance:

flatten(list(NA, list("TRUE", list(FALSE), 0L))

should return

list(NA, "TRUE", FALSE, 0L)

instead of

c(NA, "TRUE", "FALSE", "0")

which would be returned by unlist(list(list(NA, list("TRUE", list(FALSE), 0L)).

As it is seen from the example above, the flattening should be recursive. Is there a function in standard R library which achieves this, or at least some other function which can be used to easily and efficiently implement this?

**UPDATE**: I don't know if it is clear from the above, but non-lists should not be flattened, i.e. flatten(list(1:3, list(4, 5))) should return list(c(1, 2, 3), 4, 5).

## Answers

Interesting non-trivial problem!

**MAJOR UPDATE** With all that's happened, I've rewrote the answer and removed some dead ends. I also timed the various solutions on different cases.

Here's the first, rather simple but slow, solution:

flatten1 <- function(x) { y <- list() rapply(x, function(x) y <<- c(y,x)) y }

rapply lets you traverse a list and apply a function on each leaf element. Unfortunately, it works exactly as unlist with the returned values. So I ignore the result from rapply and instead I append values to the variable y by doing <<-.

Growing y in this manner is not very efficient (it's quadratic in time). So if there are many thousands of elements this will be very slow.

A more efficient approach is the following, with simplifications from @JoshuaUlrich:

flatten2 <- function(x) { len <- sum(rapply(x, function(x) 1L)) y <- vector('list', len) i <- 0L rapply(x, function(x) { i <<- i+1L; y[[i]] <<- x }) y }

Here I first find out the result length and pre-allocate the vector. Then I fill in the values.
As you can will see, this solution is *much* faster.

Here's a version of @JoshO'Brien great solution based on Reduce, but extended so it handles arbitrary depth:

flatten3 <- function(x) { repeat { if(!any(vapply(x, is.list, logical(1)))) return(x) x <- Reduce(c, x) } }

Now let the battle begin!

# Check correctness on original problem x <- list(NA, list("TRUE", list(FALSE), 0L)) dput( flatten1(x) ) #list(NA, "TRUE", FALSE, 0L) dput( flatten2(x) ) #list(NA, "TRUE", FALSE, 0L) dput( flatten3(x) ) #list(NA_character_, "TRUE", FALSE, 0L) # Time on a huge flat list x <- as.list(1:1e5) #system.time( flatten1(x) ) # Long time system.time( flatten2(x) ) # 0.39 secs system.time( flatten3(x) ) # 0.04 secs # Time on a huge deep list x <-'leaf'; for(i in 1:11) { x <- list(left=x, right=x, value=i) } #system.time( flatten1(x) ) # Long time system.time( flatten2(x) ) # 0.05 secs system.time( flatten3(x) ) # 1.28 secs

...So what we observe is that the Reduce solution is faster when the depth is low, and the rapply solution is faster when the depth is large!

As correctness goes, here are some tests:

> dput(flatten1( list(1:3, list(1:3, 'foo')) )) list(1L, 2L, 3L, 1L, 2L, 3L, "foo") > dput(flatten2( list(1:3, list(1:3, 'foo')) )) list(1:3, 1:3, "foo") > dput(flatten3( list(1:3, list(1:3, 'foo')) )) list(1L, 2L, 3L, 1:3, "foo")

Unclear what result is desired, but I lean towards the result from flatten2...

For lists that are only a few nestings deep, you could use Reduce() and c() to do something like the following. Each application of c() removes one level of nesting. **(For fully general solution, see EDITs below.)**

L <- (list(NA, list("TRUE", list(FALSE), 0L))) Reduce(c, Reduce(c, L)) [[1]] [1] NA [[2]] [1] "TRUE" [[3]] [1] FALSE [[4]] [1] 0 # TIMING TEST x <- as.list(1:4e3) system.time(flatten(x)) # Using the improved version # user system elapsed # 0.14 0.00 0.13 system.time(Reduce(c, x)) # user system elapsed # 0.04 0.00 0.03

**EDIT** Just for fun, here's a version of @Tommy's version of @JoshO'Brien's solution that **does work** for already flat lists. **FURTHER EDIT** Now @Tommy's solved that problem as well, but in a cleaner way. I'll leave this version in place.

flatten <- function(x) { x <- list(x) repeat { x <- Reduce(c, x) if(!any(vapply(x, is.list, logical(1)))) return(x) } } flatten(list(3, TRUE, 'foo')) # [[1]] # [1] 3 # # [[2]] # [1] TRUE # # [[3]] # [1] "foo"

How about this? It builds off Josh O'Brien's solution but does the recursion with a while loop instead using unlist with recursive=FALSE.

flatten4 <- function(x) { while(any(vapply(x, is.list, logical(1)))) { # this next line gives behavior like Tommy's answer; # removing it gives behavior like Josh's x <- lapply(x, function(x) if(is.list(x)) x else list(x)) x <- unlist(x, recursive=FALSE) } x }

Keeping the commented line in gives results like this (which Tommy prefers, and so do I, for that matter).

> x <- list(1:3, list(1:3, 'foo')) > dput(flatten4(x)) list(1:3, 1:3, "foo")

Output from my system, using Tommy's tests:

dput(flatten4(foo)) #list(NA, "TRUE", FALSE, 0L) # Time on a long x <- as.list(1:1e5) system.time( x2 <- flatten2(x) ) # 0.48 secs system.time( x3 <- flatten3(x) ) # 0.07 secs system.time( x4 <- flatten4(x) ) # 0.07 secs identical(x2, x4) # TRUE identical(x3, x4) # TRUE # Time on a huge deep list x <-'leaf'; for(i in 1:11) { x <- list(left=x, right=x, value=i) } system.time( x2 <- flatten2(x) ) # 0.05 secs system.time( x3 <- flatten3(x) ) # 1.45 secs system.time( x4 <- flatten4(x) ) # 0.03 secs identical(x2, unname(x4)) # TRUE identical(unname(x3), unname(x4)) # TRUE

EDIT: As for getting the depth of a list, maybe something like this would work; it gets the index for each element recursively.

depth <- function(x) { foo <- function(x, i=NULL) { if(is.list(x)) { lapply(seq_along(x), function(xi) foo(x[[xi]], c(i,xi))) } else { i } } flatten4(foo(x)) }

It's not super fast but it seems to work fine.

x <- as.list(1:1e5) system.time(d <- depth(x)) # 0.327 s x <-'leaf'; for(i in 1:11) { x <- list(left=x, right=x, value=i) } system.time(d <- depth(x)) # 0.041s

I'd imagined it being used this way:

> x[[ d[[5]] ]] [1] "leaf" > x[[ d[[6]] ]] [1] 1

But you could also get a count of how many nodes are at each depth too.

> table(sapply(d, length)) 1 2 3 4 5 6 7 8 9 10 11 1 2 4 8 16 32 64 128 256 512 3072

*Edited to address a flaw pointed out in the comments. Sadly, it just makes it even less efficient. Ah well.*

Another approach, although I'm not sure it will be more efficient than anything @Tommy has suggested:

l <- list(NA, list("TRUE", list(FALSE), 0L)) flatten <- function(x){ obj <- rapply(x,identity,how = "unlist") cl <- rapply(x,class,how = "unlist") len <- rapply(x,length,how = "unlist") cl <- rep(cl,times = len) mapply(function(obj,cl){rs <- as(obj,cl); rs}, obj, cl, SIMPLIFY = FALSE, USE.NAMES = FALSE) } > flatten(l) [[1]] [1] NA [[2]] [1] "TRUE" [[3]] [1] FALSE [[4]] [1] 0

purrr::flatten achieves that. Though it is not recursive (by design).

So applying it twice should work:

library(purrr) l <- list(NA, list("TRUE", list(FALSE), 0L)) flatten(flatten(l))

Here is an attempt at a recursive version:

flatten_recursive <- function(x) { stopifnot(is.list(x)) if (any(vapply(x, is.list, logical(1)))) Recall(purrr::flatten(x)) else x } flatten_recursive(l)

hack_list <- function(.list) { .list[['_hack']] <- function() NULL .list <- unlist(.list) .list$`_hack` <- NULL .list }