# sort

##### Sorting or Ordering Vectors

Sort (or *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 `order`

.

##### Usage

`sort(x, decreasing = FALSE, …)`# S3 method for default
sort(x, decreasing = FALSE, na.last = NA, …)

sort.int(x, partial = NULL, na.last = NA, decreasing = FALSE,
method = c("auto", "shell", "quick", "radix"), index.return = FALSE)

##### Arguments

- x
for

`sort`

an R object with a class or a numeric, complex, character or logical vector. For`sort.int`

, a numeric, complex, character or logical vector, or a factor.- decreasing
logical. Should the sort be increasing or decreasing? For the

`"radix"`

method, this can be a vector of length equal to the number of arguments in`…`

. For the other methods, it must be length one. Not available for partial sorting.- …
arguments to be passed to or from methods or (for the default methods and objects without a class) to

`sort.int`

.- na.last
for controlling the treatment of

`NA`

s. If`TRUE`

, missing values in the data are put last; if`FALSE`

, they are put first; if`NA`

, they are removed.- partial
`NULL`

or a vector of indices for partial sorting.- method
character string specifying the algorithm used. Not available for partial sorting. Can be abbreviated.

- index.return
logical indicating if the ordering index vector should be returned as well. Supported by

`method == "radix"`

for any`na.last`

mode and data type, and the other methods when`na.last = NA`

(the default) and fully sorting non-factors.

##### Details

`sort`

is a generic function for which methods can be written,
and `sort.int`

is the internal method which is compatible
with S if only the first three arguments are used.

The default `sort`

method makes use of `order`

for
classed objects, which in turn makes use of the generic function
`xtfrm`

(and can be slow unless a `xtfrm`

method has
been defined or `is.numeric(x)`

is true).

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

The `"auto"`

method selects `"radix"`

for short (less than
\(2^{31}\) elements) numeric vectors, integer vectors, logical
vectors and factors; otherwise, `"shell"`

.

Except for method `"radix"`

,
the sort order for character vectors will depend on the collating
sequence of the locale in use: see `Comparison`

.
The sort order for factors is the order of their levels (which is
particularly appropriate for ordered factors).

If `partial`

is not `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 `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 `"shell"`

uses Shellsort (an \(O(n^{4/3})\) variant from
Sedgewick (1986)). If `x`

has names a stable modification is
used, so ties are not reordered. (This only matters if names are
present.)

Method `"quick"`

uses Singleton (1969)'s implementation of
Hoare's Quicksort method and is only available when `x`

is
numeric (double or integer) and `partial`

is `NULL`

. (For
other types of `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. (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 `"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 Matt Dowle and 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 `"radix"`

method generally outperforms the other methods,
especially for character vectors and 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
`na.last`

options). The implementation is orders of magnitude
faster than shell sort for character vectors, in part thanks to clever
use of the internal `CHARSXP`

table.

However, there are some caveats with the radix sort:

If

`x`

is a`character`

vector, all elements must share the same encoding. Only UTF-8 (including ASCII) and Latin-1 encodings are supported. Collation always follows the "C" locale.Long vectors (with more than 2^32 elements) and

`complex`

vectors are not supported yet.

##### Value

For `sort`

, the result depends on the S3 method which is
dispatched. If `x`

does not have a class `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
`x[order(x, ...)]`

: this depends on the class having a suitable
method for `[`

(and also that `order`

will work,
which requires a `xtfrm`

method).

For `sort.int`

the value is the sorted vector unless
`index.return`

is true, when the result is a list with components
named `x`

and `ix`

containing the sorted numbers and the
ordering index vector. In the latter case, if ```
method ==
"quick"
```

ties may be reversed in the ordering (unlike
`sort.list`

) as quicksort is not stable. For ```
method ==
"radix"
```

, `index.return`

is supported for all `na.last`

modes. The other methods only support `index.return`

when `na.last`

is `NA`

. The index vector
refers to element numbers *after removal of NAs*: see

`order`

if you want the original element numbers.All attributes are removed from the return value (see Becker *et
al*, 1988, p.146) except names, which are sorted. (If
`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).
*The New S Language*.
Wadsworth & Brooks/Cole.

Knuth, D. E. (1998).
*The Art of Computer Programming, Volume 3: Sorting and
Searching*, 2nd ed.
Addison-Wesley.

Sedgewick, R. (1986).
A new upper bound for Shellsort.
*Journal of Algorithms*, **7**, 159--173.
10.1016/0196-6774(86)90001-5.

Singleton, R. C. (1969).
Algorithm 347: an efficient algorithm for sorting with minimal storage.
*Communications of the ACM*, **12**, 185--186.
10.1145/362875.362901.

##### See Also

‘Comparison’ for how character strings are collated.

`order`

for sorting on or reordering multiple variables.

##### Examples

`library(base)`

```
# NOT RUN {
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
# }
# NOT RUN {
## 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))
# }
```

*Documentation reproduced from package base, version 3.6.0, License: Part of R 3.6.0*