Reverse / transpose a one-to-many map in Scala - scala

Question

What is the best way to turn a Map[A, Set[B]] into a Map[B, Set[A]]?
For example, how do I turn a
Map(1 -> Set("a", "b"),
2 -> Set("b", "c"),
3 -> Set("c", "d"))
into a
Map("a" -> Set(1),
"b" -> Set(1, 2),
"c" -> Set(2, 3),
"d" -> Set(3))
(I'm using immutable collections only here. And my real problem has nothing to do with strings or integers. :)

Answer 1

with help from aioobe and Moritz:
def reverse[A, B](m: Map[A, Set[B]]) =
m.values.toSet.flatten.map(v => (v, m.keys.filter(m(_)(v)))).toMap
It's a bit more readable if you explicitly call contains:
def reverse[A, B](m: Map[A, Set[B]]) =
m.values.toSet.flatten.map(v => (v, m.keys.filter(m(_).contains(v)))).toMap

Answer 2

Best I've come up with so far is
val intToStrs = Map(1 -> Set("a", "b"),
2 -> Set("b", "c"),
3 -> Set("c", "d"))
def mappingFor(key: String) =
intToStrs.keys.filter(intToStrs(_) contains key).toSet
val newKeys = intToStrs.values.flatten
val inverseMap = newKeys.map(newKey => (newKey -> mappingFor(newKey))).toMap

Answer 3

Or another one using folds:
def reverse2[A,B](m:Map[A,Set[B]])=
m.foldLeft(Map[B,Set[A]]()){case (r,(k,s)) =>
s.foldLeft(r){case (r,e)=>
r + (e -> (r.getOrElse(e, Set()) + k))
}
}

Answer 4

Here's a one statement solution
orginalMap
.map{case (k, v)=>value.map{v2=>(v2,k)}}
.flatten
.groupBy{_._1}
.transform {(k, v)=>v.unzip._2.toSet}
This bit rather neatly (*) produces the tuples needed to construct the reverse map
Map(1 -> Set("a", "b"),
2 -> Set("b", "c"),
3 -> Set("c", "d"))
.map{case (k, v)=>v.map{v2=>(v2,k)}}.flatten
produces
List((a,1), (b,1), (b,2), (c,2), (c,3), (d,3))
Converting it directly to a map overwrites the values corresponding to duplicate keys though
Adding .groupBy{_._1} gets this
Map(c -> List((c,2), (c,3)),
a -> List((a,1)),
d -> List((d,3)),
b -> List((b,1), (b,2)))
which is closer. To turn those lists into Sets of the second half of the pairs.
.transform {(k, v)=>v.unzip._2.toSet}
gives
Map(c -> Set(2, 3), a -> Set(1), d -> Set(3), b -> Set(1, 2))
QED :)
(*) YMMV

Answer 5

A simple, but maybe not super-elegant solution:
def reverse[A,B](m:Map[A,Set[B]])={
var r = Map[B,Set[A]]()
m.keySet foreach { k=>
m(k) foreach { e =>
r = r + (e -> (r.getOrElse(e, Set()) + k))
}
}
r
}

Answer 6

The easiest way I can think of is:
// unfold values to tuples (v,k)
// for all values v in the Set referenced by key k
def vk = for {
(k,vs) <- m.iterator
v <- vs.iterator
} yield (v -> k)
// fold iterator back into a map
(Map[String,Set[Int]]() /: vk) {
// alternative syntax: vk.foldLeft(Map[String,Set[Int]]()) {
case (m,(k,v)) if m contains k =>
// Map already contains a Set, so just add the value
m updated (k, m(k) + v)
case (m,(k,v)) =>
// key not in the map - wrap value in a Set and return updated map
m updated (k, Set(v))
}