如果我知道节点及其父节点，如何构建树？

Question

说我得到了一些节点和它们的直接父节点，比如：

case class Mapping(name: String, parents: Seq[String] = Nil)

val mappings = Seq(
  Mapping("aaa"),
  Mapping("bbb"),
  Mapping("ccc"),
  Mapping("ddd", Seq("aaa", "bbb")),
  Mapping("eee", Seq("ccc")),
  Mapping("fff", Seq("ddd")),
  Mapping("ggg", Seq("aaa", "fff")),
  Mapping("hhh")
)

如何在 Scala 中编写一个基于它们构建树的函数？

def buildTrees(data: Seq[Mapping]): Seq[Node] = ???

case class Node(name: String, children: Seq[Node] = Nil)

val trees = buildTrees(mappings)

private val expectedTree = Seq(
  Node("aaa", Seq(
    Node("ggg"),
    Node("ddd", Seq(
      Node("fff", Seq(
        Node("ggg")
      ))))
  )),
  Node("bbb", Seq(
    Node("ddd", Seq(
      Node("fff", Seq(
        Node("ggg")
      ))))
  )),
  Node("ccc", Seq(
    Node("eee")
  )),
  Node("hhh", Seq())
)

if (trees == expectedTree) {
  println("OK")
} else {
  println("Not equal")
}

如何实现buildTrees方法？想了想，还是得到了一个优雅的解决方案。

更新：希望看到不可变数据的解决方案

Answer 1

def buildTrees(data: Seq[Mapping]): Seq[Node] = {
  def attachToParents(newChild: Mapping, parents: Seq[Node]): Seq[Node] = {
    for (parent <- parents) yield {
      val attachedChildren = attachToParents(newChild, parent.children)
      if (newChild.parents.contains(parent.name))
        parent.copy(children = Node(newChild.name) +: attachedChildren)
      else 
        parent.copy(children = attachedChildren)
    }
  }

  @tailrec
  def helper(xs: Seq[Mapping], accu: Seq[Node]): Seq[Node] = xs match {
    case Seq() => accu
    case head +: tail => head match {
      case Mapping(name, Seq()) => helper(tail, accu :+ Node(name))
      case Mapping(name, parents) => helper(tail, attachToParents(head, accu))
    }
  }
  helper(data, Seq())
}

Answer 2

另一个实现是：

高效
stack-not-overflowing
纯函数

.

import scala.collection.immutable.Queue

class CyclicReferences(val nodes: Seq[String])
  extends RuntimeException(f"elements withing cycle detected: ${nodes mkString ","}")

def buildTrees(data: Seq[Mapping]): Seq[Node] = {
  val parents = data.map(m => (m.name, m.parents)).toMap withDefaultValue Seq.empty
  val children = data.flatMap(m => m.parents map ((_, m.name))).groupBy(_._1).mapValues(_.map(_._2))

  def loop(queue: Queue[String], unresolved: Map[String, Set[String]], nodes: Map[String, Node]): TraversableOnce[Node] = queue match {
    case Seq() => if (unresolved.isEmpty) nodes.values else throw new CyclicReferences(unresolved.keys.toSeq)
    case key +: rest =>
      val (newQueue, newUnresolved) = ((rest, unresolved) /: parents(key)) { (pair, parent) =>
        val (queue, children) = pair
        val ch = children(parent) - key
        if (ch.isEmpty) (queue :+ parent, children - parent)
        else (queue, children.updated(parent, ch))
      }
      val node = Node(key, children.getOrElse(key, Seq.empty) map nodes)
      loop(newQueue, newUnresolved, nodes + (key -> node))
  }
  val initial = Queue(parents.keys.filter(key => !children.contains(key)).toSeq: _*)
  val unresolved = children mapValues (_.toSet) withDefaultValue Set.empty
  loop(initial, unresolved, Map()).filter(node => parents(node.name).isEmpty).toIndexedSeq
}

与xiefei方案的主要区别在于：

每个节点只构建一次，毕竟他的children已经已经构建，即没有 copy 调用
检测循环引用
所有发现都是通过高效的 Map 和 Set 操作实现的

所以它可能不是最简单的，但 50% 的生产就绪。

如果我知道节点及其父节点，如何构建树？

How to build the tree if I know nodes and their parents?

tree

scala