# Solve membership binary mask problem in Scala

Imagine you have two string sequences:

val s1 = Seq("c", "a", "b", "z", "a", "b")
val s2 = Seq("a", "b")


You need to come up with an algorithm that generates a binary membership mask of s2 in s1, e.g.:

algorithm(s1, s2) => 011000


Here are some other examples:

val s1 = Seq("a", "b", "z", "c", "a")
val s2 = Seq("a", "b", "z")
11100

val s1 = Seq("z", "b", "a", "a", "b")
val s2 = Seq("a", "b")
00011

val s1 = Seq("z", "b", "a", "a", "b")
val s2 = Seq("a")
00100

val s1 = Seq("z", "b", "a", "a", "b")
val s2 = Seq("a", "a")
00110


Notice that we only count first sequence match and discard the rest sequence matches.

Basically, in case of s2 = Seq("z", "b", "a", "a", "b") and s1 = Seq("a", "b") we are trying to solve the following task:

"z"  "b"  "a"  "a"  "b"
|    |    |    |    |
" "  " "  " "  "a"  "b"
|    |    |    |    |
0    0    0    1    1


Why? Imagine you have a sequence of auto-generated strings like "This is Google Inc ." but you only need to extract "Google" from it cutting everything else. It is easy when you know what you are searching for but once it is "This is ? Inc ." you have no way but to rely on binary masks that you collected from a big corpus. In order to generate such masks, you first need the algorithm described above.

I have come up with a simple while loop. This looks pretty ugly, so there should be another more Scala-like solution. How would you solve it?

def binmask(a: Seq[String], b: Seq[String]): String = {
val x = a.sliding(b.length, 1)
var continue = true
while (continue && x.hasNext) {
val g = x.next()
if (g == b) {
continue = false
}
}

• So this is basically a substring search, except that each "character" is a string? – 200_success Feb 21 at 22:37
• Yes, you can say so. Although I would not call it a substring but rather subsequence search since we shall split each string via whitespace. – minerals Feb 21 at 22:49
• What if s2 never occurs in s1? For example, binmask(Seq("a", "b", "a", "a", "b"), Seq("b", "b")) is "0000", which is shorter than binmask(Seq("a", "b", "a", "a", "b"), Seq("a", "a")), which is "00110". Is that intentional? – 200_success Feb 21 at 23:26
• This should not happen because you only select s2 that exist in s1 beforehand. But this is a valid point. I added another if condition. – minerals Feb 22 at 6:15

The "never occurs" bug is still there. It stems from the fact that the length of b has an inverse relationship to the length of x. Try varying the length of a non-occurring b and see what you get.

There's also the fact that this is a rather imperative approach, whereas good Scala style tries to be more functional.

When I first saw this I thought, "Doesn't indexOfSlice() offer most of what's needed?"

def binmask(seq :Seq[String], slice :Seq[String]) :String = {
val ios = seq indexOfSlice slice
if (ios < 0)
"0"*seq.length
else {
val slcLen = slice.length
"0"*ios + "1"*slcLen + "0"*(seq.length-slcLen-ios)
}
}


The slight drawback here is that indexOfSlice() will traverse the seq input until it finds a match (or completely if not found) and then seq is traversed again for its length.

The standard Scala means to achieve iteration with early termination but without mutable state, is via recursion. Preferably tail recursion, which the compiler turns into a while loop under the hood.

def binmask(seq :Seq[String], slice :Seq[String], acc :String = "") :String =
if (seq startsWith slice) {
val slcLen = slice.length
acc + "1"*slcLen + "0"*(seq.length - slcLen)
}
else if (seq.isEmpty) acc
else binmask(seq.tail, slice, acc + "0")


Some feel that making the accumulator a passed parameter (even though it is "hidden" behind a default value) exposes too much implementation in the public interface. For them, an inner recursion loop is preferable.

def binmask(seq :Seq[String], slice :Seq[String]) :String = {
def loop(subseq: Seq[String], acc: String): String =
if (subseq startsWith slice) {
val slcLen = slice.length
acc + "1" * slcLen + "0" * (subseq.length - slcLen)
}
else if (subseq.isEmpty) acc
else loop(subseq.tail, acc + "0")

loop(seq, "")
}


The function should be genericized to accept any two sequences of the same type, so that you can also write binmask("abaab", "aa") for convenience.

Recursion is a bit tedious and error-prone, as your correction in Rev 7 shows. I suggest taking advantage of Iterator.indexWhere() to perform the search.

def binmask[T](a: Seq[T], b: Seq[T]): String = a.sliding(b.length, 1).indexWhere(_ == b) match {
case -1 => "0" * a.length
case i  => "0" * i + "1" * b.length + "0" * (a.length - i - b.length)
}