**Rcpp Gallery**, and kindly contributed to R-bloggers)

Consider the problem to sort all elements of the given vector in ascending order. We can simply use the function `std::sort`

from the C++ STL.

```
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]
NumericVector stl_sort(NumericVector x) {
NumericVector y = clone(x);
std::sort(y.begin(), y.end());
return y;
}
```

```
library(rbenchmark)
set.seed(123)
z <- rnorm(100000)
x <- rnorm(100)
# check that stl_sort is the same as sort
stopifnot(all.equal(stl_sort(x), sort(x)))
# benchmark stl_sort and sort
benchmark(stl_sort(z), sort(z), order="relative")[,1:4]
```

test replications elapsed relative 1 stl_sort(z) 100 0.632 1.000 2 sort(z) 100 1.164 1.842

Consider the problem of sorting the first `n`

elements of a given vector. The function `std::partial_sort`

from the C++ STL does just this.

```
// [[Rcpp::export]]
NumericVector stl_partial_sort(NumericVector x, int n) {
NumericVector y = clone(x);
std::partial_sort(y.begin(), y.begin()+n, y.end());
return y;
}
```

An alternate implementation of a partial sort algorithm is to use `std::nth_element`

to partition the given vector at the nth sorted element and then use `std::sort`

, both from the STL, to sort the vector from the beginning to the nth element.

For an equivalent implementation in R, we can use the `sort`

function by specifying a vector of `1:n`

for the partial argument (i.e. `partial=1:n`

).

```
// [[Rcpp::export]]
NumericVector nth_partial_sort(NumericVector x, int nth) {
NumericVector y = clone(x);
std::nth_element(y.begin(), y.begin()+nth, y.end());
std::sort(y.begin(), y.begin()+nth);
return y;
}
```

```
n <- 25000
# check that stl_partial_sort is equal to nth_partial_sort
stopifnot(all.equal(stl_partial_sort(x, 50)[1:50],
nth_partial_sort(x, 50)[1:50]))
# benchmark stl_partial_sort, nth_element_sort, and sort
benchmark(stl_partial_sort(z, n),
nth_partial_sort(z, n),
sort(z, partial=1:n),
order="relative")[,1:4]
```

test replications elapsed relative 2 nth_partial_sort(z, n) 100 0.208 1.000 1 stl_partial_sort(z, n) 100 0.516 2.481 3 sort(z, partial = 1:n) 100 0.796 3.827

An interesting result to note is the gain in speed of `nth_partial_sort`

over `stl_partial_sort`

. In this case, for the given data, it is faster to use the combination of`std::nth_element`

and `std::sort`

rather than `std::partial_sort`

to sort the first `n`

elements of a vector.

```
// [[Rcpp::export]]
NumericVector stl_nth_element(NumericVector x, int n) {
NumericVector y = clone(x);
std::nth_element(y.begin(), y.begin()+n, y.end());
return y;
}
```

Finally, consider a problem where you only need a single element of a sorted vector. The function `std::nth_element`

from the C++ STL does just this. An example of this type of problem is computing the median of a given vector.

For an equivalent implementation in R, we can use the `sort`

function by specifying a scalar value for the argument partial (i.e. `partial=n`

).

```
# check that the nth sorted elements of the vectors are equal
stopifnot(all.equal(stl_nth_element(x, 43)[43], sort(x, partial=43)[43]))
# benchmark nth_element and sort
benchmark(stl_nth_element(z, n),
sort(z, partial=n),
order="relative")[,1:4]
```

test replications elapsed relative 1 stl_nth_element(z, n) 100 0.089 1.000 2 sort(z, partial = n) 100 0.238 2.674

While these are not huge speed improvements over the base R sort function, this post demonstrates how to easily access sorting functions in the C++ STL and is a good exercise to better understand the differences and performance of the sorting algorithms available in C++ and R.

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