# List Comprehensions in R

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List comprehensions in Python or Haskell are popular and useful tools to filter a list given some predicates. The `foreach`

package by Revolution Analytics gives us a handy interface to list comprehensions in R.

Quicksort is a recursive algorithm to sort a list. In Haskell, quicksort looks very clean and elegant using list comprehensions (from Learn You a Haskell for Great Good!):

quicksort :: (Ord a) => [a] -> [a] quicksort [] = [] quicksort (x:xs) = let smallerSorted = quicksort [a | a <- xs, a <= x] biggerSorted = quicksort [a | a <- xs, a > x] in smallerSorted ++ [x] ++ biggerSorted

Quicksort takes the first element of a list and puts all smaller elements on the left of the item and all larger elements to the right. It recursively calls `quicksort`

again on those sublists (`smallerSorted`

and `biggerSorted`

). The list comprehension `[a | a <- xs, a < x]`

takes a list as an input and filters out all elements that are smaller than \(x\), whereas `[a | a <- xs, a > x]`

filters out all elements that are larger than \(x\).

```
ghci> quicksort [10,2,5,3,1,6,7,4,2,3,4,8,9]
[1,2,2,3,3,4,4,5,6,7,8,9,10]
```

Using `foreach`

, the same algorithm in R looks like this (from the `foreach`

vignette):

library(foreach) qsort <- function(x) { n <- length(x) if (n == 0) { x } else { p <- sample(n, 1) smaller <- foreach(y=x[-p], .combine=c) %:% when(y <= x[p]) %do% y larger <- foreach(y=x[-p], .combine=c) %:% when(y > x[p]) %do% y c(qsort(smaller), x[p], qsort(larger)) } }

Not quite as concise as Haskell, but close!

> qsort(c(10,2,5,3,1,6,7,4,2,3,4,8,9)) [1] 1 2 2 3 3 4 4 5 6 7 8 9 10

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