Find all possible increasing subsequences of a given length in Scala - scala

Question

What is the efficient way to find all possible increasing sub-sequences of a given length in Scala?
For eg: Suppose there is a sequence of numbers as follows:
7 6 9 11 16 10 12
The possible increasing subsequences of size 3 for the above sequence are :
7 9 11
7 9 16
7 9 10
7 9 12
7 11 16
7 11 12
7 10 12
6 9 11
6 9 16
etc…
I would like to know which Scala data structures would help in finding the sub-sequences quickly.

Answer 1

This is a Scala solution to your question:
def subSequence[A](list: List[A], size: Int)(implicit ord: Ordering[A]): List[List[A]] =
if (size <= 1) {
list.map(List(_))
} else {
( for {
t1 <- list.tails if t1.length >= size - 1
a = t1.head
t2 <- subSequence(t1.tail, size - 1)
b = t2.head if ord.lt(a, b)
} yield a :: t2
).toList
}
Hopefully someone else will provide a tail-recursive version of this which should perform better.

Answer 2

This is one possible solution.
val l = List(7, 6, 9, 11, 16, 10, 12)
l.combinations(3).filter(x => x == x.sorted) // this gives the desired result for size 3 and `3` can be changed to some number `n` for different size of combinations.
I just created combinations and filtered later which might not be very efficient.But, I am interested to know more efficient answers by generating only increasing combinations.