% File src/library/base/man/sort.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2022 R Core Team
% Distributed under GPL 2 or later

\name{sort}
\alias{sort}
\alias{sort.default}
\alias{sort.POSIXlt}
\alias{sort.int}
\title{Sorting or Ordering Vectors}
\description{
  Sort (or \emph{order}) a vector or factor (partially) into
  ascending or descending order.  For ordering along more than one
  variable, e.g., for sorting data frames, see \code{\link{order}}.
}
\usage{
sort(x, decreasing = FALSE, \dots)

\method{sort}{default}(x, decreasing = FALSE, na.last = NA, \dots)

sort.int(x, partial = NULL, na.last = NA, decreasing = FALSE,
         method = c("auto", "shell", "quick", "radix"), index.return = FALSE)
}
\arguments{
  \item{x}{for \code{sort} an \R object with a class or a numeric,
    complex, character or logical vector.  For \code{sort.int}, a
    numeric, complex, character or logical vector, or a factor.}
  \item{decreasing}{logical.  Should the sort be increasing or decreasing?
    Not available for partial sorting.}
  \item{\dots}{arguments to be passed to or from methods or (for the
    default methods and objects without a class) to \code{sort.int}.}
  \item{na.last}{for controlling the treatment of \code{NA}s.
    If \code{TRUE}, missing values in the data are put last; if
    \code{FALSE}, they are put first; if \code{NA}, they are removed.}
  \item{partial}{\code{NULL} or a  vector of indices for partial sorting.}
  \item{method}{character string specifying the algorithm used.  Not
    available for partial sorting.  Can be abbreviated.}
  \item{index.return}{logical indicating if the ordering index vector should
    be returned as well. Supported by \code{method == "radix"} for any
    \code{na.last} mode and data type, and the other methods when
    \code{na.last = NA} (the default) and fully sorting non-factors.}
}
\details{
  \code{sort} is a generic function for which methods can be written,
  and \code{sort.int} is the internal method which is compatible
  with S if only the first three arguments are used.

  The default \code{sort} method makes use of \code{\link{order}} for
  classed objects, which in turn makes use of the generic function
  \code{\link{xtfrm}} (and can be slow unless a \code{xtfrm} method has
  been defined or \code{\link{is.numeric}(x)} is true).

  Complex values are sorted first by the real part, then the imaginary
  part.

  The \code{"auto"} method selects \code{"radix"} for short (less than
  \eqn{2^{31}}{2^31} elements) numeric vectors, integer vectors, logical
  vectors and factors; otherwise, \code{"shell"}.
  
  Except for method \code{"radix"},
  the sort order for character vectors will depend on the collating
  sequence of the locale in use: see \code{\link{Comparison}}.
  The sort order for factors is the order of their levels (which is
  particularly appropriate for ordered factors).


  If \code{partial} is not \code{NULL}, it is taken to contain indices
  of elements of the result which are to be placed in their correct
  positions in the sorted array by partial sorting.  For each of the
  result values in a specified position, any values smaller than that
  one are guaranteed to have a smaller index in the sorted array and any
  values which are greater are guaranteed to have a bigger index in the
  sorted array.  (This is included for efficiency, and many of the
  options are not available for partial sorting.  It is only
  substantially more efficient if \code{partial} has a handful of
  elements, and a full sort is done (a Quicksort if possible) if there
  are more than 10.)  Names are discarded for partial sorting.

  Method \code{"shell"} uses Shellsort (an \eqn{O(n^{4/3})} variant from
  \bibcite{Sedgewick (1986)}).  If \code{x} has names a stable modification is
  used, so ties are not reordered.  (This only matters if names are
  present.)

  Method \code{"quick"} uses Singleton (1969)'s implementation of
  \I{Hoare}'s Quicksort method and is only available when \code{x} is
  numeric (double or integer) and \code{partial} is \code{NULL}.  (For
  other types of \code{x} Shellsort is used, silently.)  It is normally
  somewhat faster than Shellsort (perhaps 50\% faster on vectors of
  length a million and twice as fast at a billion) but has poor
  performance in the rare worst case.  (\I{Peto}'s modification using a
  pseudo-random midpoint is used to make the worst case rarer.)  This is
  not a stable sort, and ties may be reordered.
  
  Method \code{"radix"} relies on simple hashing to scale time linearly
  with the input size, i.e., its asymptotic time complexity is O(n). The
  specific variant and its implementation originated from the data.table
  package and are due to \I{Matt Dowle} and \I{Arun Srinivasan}.  For small
  inputs (< 200), the implementation uses an insertion sort (O(n^2))
  that operates in-place to avoid the allocation overhead of the radix
  sort. For integer vectors of range less than 100,000, it switches to a
  simpler and faster linear time counting sort. In all cases, the sort
  is stable; the order of ties is preserved. It is the default method
  for integer vectors and factors.

  The \code{"radix"} method generally outperforms the other methods,
  especially for small integers.  Compared to quick sort, it is slightly
  faster for vectors with large integer or real values (but unlike quick
  sort, radix is stable and supports all \code{na.last} options). The
  implementation is orders of magnitude faster than shell sort for
  character vectors, but collation \emph{does not respect the
  locale} and so gives incorrect answers even in English locales.

  However, there are some caveats for the radix sort:
  \itemize{
    \item
      If \code{x} is a \code{character} vector, all elements must share
      the same encoding.  Only UTF-8 (including ASCII) and Latin-1
      encodings are supported.  Collation follows that with
      \env{LC_COLLATE=C}, that is lexicographically byte-by-byte using
      numerical ordering of bytes.
    \item
      \link{Long vectors} (with \eqn{2^{31}}{2^31} or more elements)
      and \code{complex} vectors are not supported.
  }
}

\value{
  For \code{sort}, the result depends on the S3 method which is
  dispatched.  If \code{x} does not have a class \code{sort.int} is used
  and it description applies.  For classed objects which do not have a
  specific method the default method will be used and is equivalent to
  \code{x[order(x, ...)]}: this depends on the class having a suitable
  method for \code{[} (and also that \code{\link{order}} will work,
  which requires a \code{\link{xtfrm}} method).

  For \code{sort.int} the value is the sorted vector unless
  \code{index.return} is true, when the result is a list with components
  named \code{x} and \code{ix} containing the sorted numbers and the
  ordering index vector.  In the latter case, if \code{method ==
    "quick"} ties may be reversed in the ordering (unlike
  \code{sort.list}) as quicksort is not stable.  For \code{method ==
  "radix"}, \code{index.return} is supported for all \code{na.last}
  modes. The other methods only support \code{index.return}
  when \code{na.last} is \code{NA}. The index vector
  refers to element numbers \emph{after removal of \code{NA}s}: see
  \code{\link{order}} if you want the original element numbers.

  All attributes are removed from the return value (see Becker
  \abbr{et al.}, 1988, p.146) except names, which are sorted.  (If
  \code{partial} is specified even the names are removed.)  Note that
  this means that the returned value has no class, except for factors
  and ordered factors (which are treated specially and whose result is
  transformed back to the original class).
}

\references{
  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988).
  \emph{The New S Language}.
  Wadsworth & Brooks/Cole.

  Knuth, D. E. (1998).
  \emph{The Art of Computer Programming, Volume 3: Sorting and
    Searching}, 2nd ed.
  Addison-Wesley.
  
  Sedgewick, R. (1986).
  A new upper bound for Shellsort.
  \emph{Journal of Algorithms}, \bold{7}, 159--173.
  \doi{10.1016/0196-6774(86)90001-5}.

  Singleton, R. C. (1969).
  Algorithm 347: an efficient algorithm for sorting with minimal storage.
  \emph{Communications of the ACM}, \bold{12}, 185--186.
  \doi{10.1145/362875.362901}.
}
\seealso{
  \sQuote{\link{Comparison}} for how character strings are collated.

  \code{\link{order}} for sorting on or reordering multiple variables.

  \code{\link{is.unsorted}}. \code{\link{rank}}.
}
\examples{
require(stats)

x <- swiss$Education[1:25]
x; sort(x); sort(x, partial = c(10, 15))

## illustrate 'stable' sorting (of ties):
sort(c(10:3, 2:12), method = "shell", index.return = TRUE) # is stable
## $x : 2  3  3  4  4  5  5  6  6  7  7  8  8  9  9 10 10 11 12
## $ix: 9  8 10  7 11  6 12  5 13  4 14  3 15  2 16  1 17 18 19
sort(c(10:3, 2:12), method = "quick", index.return = TRUE) # is not
## $x : 2  3  3  4  4  5  5  6  6  7  7  8  8  9  9 10 10 11 12
## $ix: 9 10  8  7 11  6 12  5 13  4 14  3 15 16  2 17  1 18 19

x <- c(1:3, 3:5, 10)
is.unsorted(x)                  # FALSE: is sorted
is.unsorted(x, strictly = TRUE) # TRUE : is not (and cannot be)
                                # sorted strictly
\dontrun{
## Small speed comparison simulation:
N <- 2000
Sim <- 20
rep <- 1000 # << adjust to your CPU
c1 <- c2 <- numeric(Sim)
for(is in seq_len(Sim)){
  x <- rnorm(N)
  c1[is] <- system.time(for(i in 1:rep) sort(x, method = "shell"))[1]
  c2[is] <- system.time(for(i in 1:rep) sort(x, method = "quick"))[1]
  stopifnot(sort(x, method = "shell") == sort(x, method = "quick"))
}
rbind(ShellSort = c1, QuickSort = c2)
cat("Speedup factor of quick sort():\n")
summary({qq <- c1 / c2; qq[is.finite(qq)]})

## A larger test
x <- rnorm(1e7)
system.time(x1 <- sort(x, method = "shell"))
system.time(x2 <- sort(x, method = "quick"))
system.time(x3 <- sort(x, method = "radix"))
stopifnot(identical(x1, x2))
stopifnot(identical(x1, x3))
}}
\keyword{univar}
\keyword{manip}
\keyword{arith}
