Scala Hacking: Computing Powerset

Given a set represented as a String, we can compute its powerset using foldLeft, as shown below.

def powerset(s: String) =
s.foldLeft(Set("")) {
case (acc, x) => acc ++ acc.map(_ + x)
}
view raw powerset.scala hosted with ❤ by GitHub

Isn’t this approach quite concise and elegant? Following snippet shows a pretty-printed output from powerset for a set: "abc".

scala> powerset("abc").toList sortWith ( _ < _) mkString "\n"

res3: String = "
| a
| ab
| abc
| ac
| b
| bc
| c"

Following is a F# implementation of this same function.

let powerset (s:string): Set<string> =
s.ToCharArray()
|> Array.fold(
fun (acc: Set<string>) x -> acc + (Set.map(fun y -> x.ToString()+y) acc)
) (Set.empty.Add(""))
view raw powerset.fs hosted with ❤ by GitHub

Scala Hacking: Computing min and max of a List

There are several ways to accomplish this. Next code snippet shows how to compute min and max using reduceLeft.

val ls = List(1,2,3,4,5)

ls.reduceLeft(_ min _) // is equivalent to ls.min

ls.reduceLeft(_ max _) // is equivalent to ls.max

Same can be accomplished via foldLeft or foldRight.

ls.foldLeft(Int.MaxValue) (_ min _)

ls.foldLeft(Int.MinValue) (_ max _)

However, can we compute both min and max in one line? Check out the following snippet.

ls.map(
x=>(x,x)).reduceLeft(
(x,y) => (x._1 min y._1, x._2 max y._2)

An alternative is to use foldLeft:

ls.foldLeft
((Int.MaxValue, Int.MinValue))
((acc:(Int,Int),y:Int) => (acc._1 min y, acc._2 max y))

Constructing a balanced Binary Search Tree from a sorted List in O(N) time

This post discusses a O(n) algorithm that construct a balanced binary search tree (BST) from a sorted list. For instance, consider that we are given a sorted list: [1,2,3,4,5,6,7]. We have to construct a balanced BST as follows.

        4
        |
    2        6 
    |        |
  1   3   5     7

To do so, we use the following definition of Tree, described in Scala By Example book.

abstract class IntSet
case object Empty extends IntSet
case class NonEmpty(elem: Int, left: IntSet, right: IntSet) extends IntSet

One straight-forward approach would be to repeatedly perform binary search on the given list to find the median of the list, and then, to construct a balanced BST recursively. Complexity of such approach is O(nlogn), where n is the number of elements in the given list.

A better algorithm constructs balanced BST while iterating the list only once. It begins with the leaf nodes and construct the tree in a bottom-up manner. As such, it avoids repeated binary searches and achieves better runtime complexity (i.e., O(n), where n is the total number of elements in the given list). Following Scala code outlines this algorithm, which effectively converts a list ls to an IntSet, a balanced BST:

def toTree(ls: List[Int]): IntSet = {
def toTreeAux(ls: List[Int], n: Int): (List[Int], IntSet) = {
if (n <= 0)
(ls, Empty)
else {
val (lls, lt) = toTreeAux(ls, n / 2) // construct left sub-tree
val x :: xs = lls // extract root node
val (xr, rt) = toTreeAux(xs, n - n / 2 - 1) // construct right sub-tree
(xr, IntSet(x, lt, rt)) // construct tree
}
}
val (ls_1, tree) = toTreeAux(ls, List.length(ls))
tree
}
view raw toTree.scala hosted with ❤ by GitHub

Any comment or query regarding this post is highly appreciated. Thanks.

“Functional Scala” by Mario Gleichmann

"Functional Scala" is a set of tutorials on Scala programming language by Mario Gleichmann. Although a bit verbose, it introduces the key constructs of Scala, and outlines Scala’s primary features from the perspective of functional programming.

Welcome to the first part of a series of episodes about ‘Functional Scala’. While positioning itself as a so called object-functional language, most of the discussion and articles about Scala centered around its object oriented features so far. If you’re reading this, chances are you want to learn more about the functional side of Scala. Well, you’ve come to the right place.

The idea for the following episodes arose out of some talks i gave about ‘Functional Scala’. I decided to write and talk about it because I wanted to solidify my own knowledge about Functional Programming in general and about Scala in particular … and because I thought I could help some people new to Scala to learn its functional features from my perspective.

Not least, there were some critical discussions in the past whether Scala is rightfully characterized as a functional Language. For this to decide, we firstly have to be clear about the core ideas, you’ll regularly come across within widely accepted functional Languages, like Haskell. We’re going to see if and how they are offered in Scala and try to push them to its limits. So without any further ado, let’s enter the world of Functional Programming (FP) in Scala.

Cheers!