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#' Enumerate the Combinations or Permutations of the Elements of a Vector
#'
#' \code{combinations} enumerates the possible combinations of a specified size
#' from the elements of a vector. \code{permutations} enumerates the possible
#' permutations.
#'
#' Caution: The number of combinations and permutations increases rapidly with
#' \code{n} and \code{r}!.
#'
#' To use values of \code{n} above about 45, you will need to increase R's
#' recursion limit. See the \code{expression} argument to the \code{options}
#' command for details on how to do this.
#'
#' @aliases combinations permutations
#' @param n Size of the source vector
#' @param r Size of the target vectors
#' @param v Source vector. Defaults to \code{1:n}
#' @param set Logical flag indicating whether duplicates should be removed from
#' the source vector \code{v}. Defaults to \code{TRUE}.
#' @param repeats.allowed Logical flag indicating whether the constructed
#' vectors may include duplicated values. Defaults to \code{FALSE}.
#' @return Returns a matrix where each row contains a vector of length
#' \code{r}.
#' @author Original versions by Bill Venables
#' \email{Bill.Venables@@cmis.csiro.au}. Extended to handle
#' \code{repeats.allowed} by Gregory R. Warnes \email{greg@@warnes.net}.
#' @seealso \code{\link[base]{choose}}, \code{\link[base]{options}}
#' @references Venables, Bill. "Programmers Note", R-News, Vol 1/1, Jan. 2001.
#' \url{https://cran.r-project.org/doc/Rnews/}
#' @keywords manip
#'
#' @details
#'
#' Taken from an email by Brian D Ripley <ripley@stats.ox.ac.uk> to r-help
#' dated Tue, 14 Dec 1999 11:14:04 +0000 (GMT) in response to
#' Alex Ahgarin \email{datamanagement@email.com}. Original version was
#' named "subsets" and was Written by Bill Venables.
#'
#' @examples
#'
#' combinations(3,2,letters[1:3])
#' combinations(3,2,letters[1:3],repeats=TRUE)
#'
#' permutations(3,2,letters[1:3])
#' permutations(3,2,letters[1:3],repeats=TRUE)
#'
#' \dontrun{
#' # To use large 'n', you need to change the default recusion limit
#' options(expressions=1e5)
#' cmat <- combinations(300,2)
#' dim(cmat) # 44850 by 2
#' }
#'
#' @export
combinations <- function(n, r, v = 1:n, set = TRUE, repeats.allowed=FALSE)
{
if(mode(n) != "numeric" || length(n) != 1
|| n < 1 || (n %% 1) != 0) stop("bad value of n")
if(mode(r) != "numeric" || length(r) != 1
|| r < 1 || (r %% 1) != 0) stop("bad value of r")
if(!is.atomic(v) || length(v) < n)
stop("v is either non-atomic or too short")
if( (r > n) & repeats.allowed==FALSE)
stop("r > n and repeats.allowed=FALSE")
if(set) {
v <- unique(sort(v))
if (length(v) < n) stop("too few different elements")
}
v0 <- vector(mode(v), 0)
## Inner workhorse
if(repeats.allowed)
sub <- function(n, r, v)
{
if(r == 0) v0 else
if(r == 1) matrix(v, n, 1) else
if(n == 1) matrix(v, 1, r) else
rbind( cbind(v[1], Recall(n, r-1, v)),
Recall(n-1, r, v[-1]))
}
else
sub <- function(n, r, v)
{
if(r == 0) v0 else
if(r == 1) matrix(v, n, 1) else
if(r == n) matrix(v, 1, n) else
rbind(cbind(v[1], Recall(n-1, r-1, v[-1])),
Recall(n-1, r, v[-1]))
}
sub(n, r, v[1:n])
}
##
## Original version by Bill Venables and cited by by Matthew
## Wiener (mcw@ln.nimh.nih.gov) in an email to R-help dated
## Tue, 14 Dec 1999 09:11:32 -0500 (EST) in response to
## Alex Ahgarin <datamanagement@email.com>
##
##
#' @rdname combinations
#' @export
permutations <- function(n, r, v = 1:n, set = TRUE, repeats.allowed=FALSE)
{
if(mode(n) != "numeric" || length(n) != 1
|| n < 1 || (n %% 1) != 0) stop("bad value of n")
if(mode(r) != "numeric" || length(r) != 1
|| r < 1 || (r %% 1) != 0) stop("bad value of r")
if(!is.atomic(v) || length(v) < n)
stop("v is either non-atomic or too short")
if( (r > n) & repeats.allowed==FALSE)
stop("r > n and repeats.allowed=FALSE")
if(set) {
v <- unique(sort(v))
if (length(v) < n) stop("too few different elements")
}
v0 <- vector(mode(v), 0)
## Inner workhorse
if(repeats.allowed)
sub <- function(n, r, v)
{
if(r==1) matrix(v,n,1) else
if(n==1) matrix(v,1,r) else
{
inner <- Recall(n, r-1, v)
cbind( rep( v, rep(nrow(inner),n) ),
matrix( t(inner), ncol=ncol(inner), nrow=nrow(inner) * n ,
byrow=TRUE )
)
}
}
else
sub <- function(n, r, v)
{
if(r==1) matrix(v,n,1) else
if(n==1) matrix(v,1,r) else
{
X <- NULL
for(i in 1:n)
X <- rbind( X, cbind( v[i], Recall(n-1, r - 1, v[-i])))
X
}
}
sub(n, r, v[1:n])
}
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