org.specs2.data.HopcroftKarp.scala Maven / Gradle / Ivy
package org.specs2
package data
import scala.collection.mutable
/**
* Hopcroft-Karp (https://en.wikipedia.org/wiki/Hopcroft%E2%80%93Karp_algorithm) algorithm for
* finding the maximum matching in a bipartite graph
*/
object HopcroftKarp {
def findMaximalMatching(vertex1: Seq[Int], vertex2: Seq[Int], edges: Map[Int, Seq[Int]]): List[(Int, Int)] = {
val nil = -1
val queue: mutable.Queue[Int] = new mutable.Queue[Int]
val dist: mutable.Map[Int, Int] = new mutable.HashMap[Int, Int]
val pair1: mutable.Map[Int, Int] = new mutable.HashMap[Int, Int]
val pair2: mutable.Map[Int, Int] = new mutable.HashMap[Int, Int]
def bfs: Boolean = {
vertex1.foreach { v =>
if (pair1(v) == nil) {
dist.put(v, 0)
queue.enqueue(v)
} else dist.put(v, Int.MaxValue)
}
dist.put(nil, Int.MaxValue)
while (queue.nonEmpty) {
val v = queue.dequeue
if (dist(v) < dist(nil)) {
edges.get(v).toSeq.flatten.foreach { u =>
if (dist(pair2(u)) == Int.MaxValue) {
dist.put(pair2(u), dist(v) + 1)
queue.enqueue(pair2(u))
}
}
}
}
dist(nil) != Int.MaxValue
}
def dfs(v: Int): Boolean = {
if (v != -1) {
edges.get(v).toSeq.flatten.foreach { u =>
if (dist(pair2(u)) == dist(v) + 1 && dfs(pair2(u))) {
pair2.put(u, v)
pair1.put(v, u)
return true
}
}
dist.put(v, Int.MaxValue)
false
} else true
}
((vertex1 ++ vertex2) :+ nil).foreach { v =>
pair1.put(v, nil)
pair2.put(v, nil)
}
var matching = 0
while (bfs) {
vertex1.foreach { v =>
if (pair1(v) == nil && dfs(v))
matching = matching + 1
}
}
pair1.toList.filterNot(_._2 == nil)
}
}