# sort: Sorting or Ordering Vectors

## Description

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

 ```1 2 3 4 5 6 7``` ```sort(x, decreasing = FALSE, ...) ## Default S3 method: 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 `NA`s: 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. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("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. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.1145/362875.362901")}.

`order` for sorting on or reordering multiple variables.
`is.unsorted`. `rank`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42``` ```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)) ## End(Not run) ```