Scala - increasing prefix of a sequence - scala

Question

I was wondering what is the most elegant way of getting the increasing prefix of a given sequence. My idea is as follows, but it is not purely functional or any elegant:
val sequence = Seq(1,2,3,1,2,3,4,5,6)
var currentElement = sequence.head - 1
val increasingPrefix = sequence.takeWhile(e =>
if (e > currentElement) {
currentElement = e
true
} else
false)
The result of the above is:
List(1,2,3)

Answer 1

You can take your solution, #Samlik, and effectively zip in the currentElement variable, but then map it out when you're done with it.
sequence.take(1) ++ sequence.zip(sequence.drop(1)).
takeWhile({case (a, b) => a < b}).map({case (a, b) => b})
Also works with infinite sequences:
val sequence = Seq(1, 2, 3).toStream ++ Stream.from(1)
sequence is now an infinite Stream, but we can peek at the first 10 items:
scala> sequence.take(10).toList
res: List[Int] = List(1, 2, 3, 1, 2, 3, 4, 5, 6, 7)
Now, using the above snippet:
val prefix = sequence.take(1) ++ sequence.zip(sequence.drop(1)).
takeWhile({case (a, b) => a < b}).map({case (a, b) => b})
Again, prefix is a Stream, but not infinite.
scala> prefix.toList
res: List[Int] = List(1, 2, 3)
N.b.: This does not handle the cases when sequence is empty, or when the prefix is also infinite.

Answer 2

If by elegant you mean concise and self-explanatory, it's probably something like the following:
sequence.inits.dropWhile(xs => xs != xs.sorted).next
inits gives us an iterator that returns the prefixes longest-first. We drop all the ones that aren't sorted and take the next one.
If you don't want to do all that sorting, you can write something like this:
sequence.scanLeft(Some(Int.MinValue): Option[Int]) {
case (Some(last), i) if i > last => Some(i)
case _ => None
}.tail.flatten
If the performance of this operation is really important, though (it probably isn't), you'll want to use something more imperative, since this solution still traverses the entire collection (twice).

Answer 3

And, another way to skin the cat:
val sequence = Seq(1,2,3,1,2,3,4,5,6)
sequence.head :: sequence
.sliding(2)
.takeWhile{case List(a,b) => a <= b}
.map(_(1)).toList
// List[Int] = List(1, 2, 3)

Answer 4

I will interpret elegance as the solution that most closely resembles the way we humans think about the problem although an extremely efficient algorithm could also be a form of elegance.
val sequence = List(1,2,3,2,3,45,5)
val increasingPrefix = takeWhile(sequence, _ < _)
I believe this code snippet captures the way most of us probably think about the solution to this problem.
This of course requires defining takeWhile:
/**
* Takes elements from a sequence by applying a predicate over two elements at a time.
* #param xs The list to take elements from
* #param f The predicate that operates over two elements at a time
* #return This function is guaranteed to return a sequence with at least one element as
* the first element is assumed to satisfy the predicate as there is no previous
* element to provide the predicate with.
*/
def takeWhile[A](xs: Traversable[A], f: (Int, Int) => Boolean): Traversable[A] = {
// function that operates over tuples and returns true when the predicate does not hold
val not = f.tupled.andThen(!_)
// Maybe one day our languages will be better than this... (dependant types anyone?)
val twos = sequence.sliding(2).map{case List(one, two) => (one, two)}
val indexOfBreak = twos.indexWhere(not)
// Twos has one less element than xs, we need to compensate for that
// An intuition is the fact that this function should always return the first element of
// a non-empty list
xs.take(i + 1)
}