1

我正在尝试将tarjan 算法的递归 python 代码转换为 scala,尤其是这部分:

def tarjan_recursive(g):
        S = []
        S_set = set()
        index = {}
        lowlink = {}
        ret = []
        def visit(v):
                index[v] = len(index)
                lowlink[v] = index[v]
                S.append(v)
                S_set.add(v)

                for w in g.get(v,()):
                        print(w)
                        if w not in index:
                                visit(w)
                                lowlink[v] = min(lowlink[w], lowlink[v])
                        elif w in S_set:
                                lowlink[v] = min(lowlink[v], index[w])
                if lowlink[v] == index[v]:
                        scc = []
                        w = None
                        while v != w:
                                w = S.pop()
                                scc.append(w)
                                S_set.remove(w)
                        ret.append(scc)

        for v in g:
                print(index)
                if not v in index:
                        visit(v)
        return ret

我知道 scala herehere中有 tarjan 算法,但它没有返回好的结果并从 python 翻译它帮助我理解它。

这是我所拥有的:

def tj_recursive(g: Map[Int,List[Int]])= {
        var s : mutable.ListBuffer[Int] = new mutable.ListBuffer()
        var s_set : mutable.Set[Int] = mutable.Set()
        var index : mutable.Map[Int,Int] =  mutable.Map()
        var lowlink : mutable.Map[Int,Int]=  mutable.Map()
        var ret : mutable.Map[Int,mutable.ListBuffer[Int]]= mutable.Map()

        def visit(v: Int):Int = {
                 index(v) = index.size
               lowlink(v) = index(v)
               var zz :List[Int]= gg.get(v).toList(0)
                            for( w <- zz) {
                  if( !(index.contains(w)) ){
                     visit(w)
                     lowlink(v) = List(lowlink(w),lowlink(v)).min
                   }else if(s_set.contains(w)){
                     lowlink(v)=List(lowlink(v),index(w)).min
                   }
               }

               if(lowlink(v)==index(v)){
                  var scc:mutable.ListBuffer[Int] = new mutable.ListBuffer()
                  var w:Int=null.asInstanceOf[Int]
                  while(v!=w){
                    w= s.last
                    scc+=w
                    s_set-=w
                  }
           ret+=scc
        }
        }

   for( v <- g) {if( !(index.contains(v)) ){visit(v)}}
   ret
}

我知道这根本不是 scala 方式(而且不干净......),但我计划在第一个版本工作时慢慢将其更改为更实用的样式。

现在,我得到了这个错误:

type mismatch;  found   : Unit  required: Int

在这条线上

if(lowlink(v)==index(v)){ 

我认为它来自这条线,但我不确定:

if( !(index.contains(w)) 

但是调试它真的很难,因为我不能只打印我的错误......

谢谢 !

4

3 回答 3

2

这是 Python 的相当直译:

def tj_recursive(g: Map[Int, List[Int]])= {
  val s = mutable.Buffer.empty[Int]
  val s_set = mutable.Set.empty[Int]
  val index = mutable.Map.empty[Int, Int]
  val lowlink = mutable.Map.empty[Int, Int]
  val ret = mutable.Buffer.empty[mutable.Buffer[Int]]

  def visit(v: Int): Unit = {
    index(v) = index.size
    lowlink(v) = index(v)
    s += v
    s_set += v

    for (w <- g(v)) {
      if (!index.contains(w)) {
        visit(w)
        lowlink(v) = math.min(lowlink(w), lowlink(v))
      } else if (s_set(w)) {
        lowlink(v) = math.min(lowlink(v), index(w))
      }
    }

    if (lowlink(v) == index(v)) {
      val scc = mutable.Buffer.empty[Int]
      var w = -1

      while(v != w) {
        w = s.remove(s.size - 1)
        scc += w
        s_set -= w
      }

      ret += scc
    }
  }

  for (v <- g.keys) if (!index.contains(v)) visit(v)
  ret
}

它在例如:

tj_recursive(Map(
  1 -> List(2),    2 -> List(1, 5), 3 -> List(4),
  4 -> List(3, 5), 5 -> List(6),    6 -> List(7),
  7 -> List(8),    8 -> List(6, 9), 9 -> Nil
))

您的实现的最大问题是visit(应该是Unit,不是Int)的返回类型以及您在最终理解中迭代图形的项目而不是图形的键这一for事实,但我已经做了一些其他的样式和清晰度的编辑(同时仍保持基本形状)。

于 2013-08-17T15:37:48.260 回答
0

这是一个迭代版本。它是Wikipedia中算法的递归版本的翻译。

case class Arc[A](from:A, to:A)

class SparseDG[A](src: Iterable[Arc[A]]) {

  val verts = (src.map(_.from) ++ src.map(_.to)).toSet.toIndexedSeq
  val qVert = verts.size
  val vertMap = verts.zipWithIndex.toMap
  val indexedSrc = src.map{ arc => Arc(vertMap(arc.from), vertMap(arc.to)) }

  val exit  = (0 until qVert)
              .map(v => indexedSrc.filter(_.from == v).map(_.to).toIndexedSeq)


  lazy val tarjan_iterative: Seq[Seq[A]] = {
    trait Step
    case object SetDepth           extends Step
    case object ConsiderSuccessors extends Step
    case object CalcLowlink        extends Step
    case object PopIfRoot          extends Step
    case class StackFrame(v:Int, next:Step)

    val result = Buffer[Seq[A]]()
    val index = new Array[Int](qVert).map(_ => -1)   // -1 = undefined
    val lowlink = new Array[Int](qVert).map(_ => -1) // -1 = undefined
    val wIndex = new Array[Int](qVert)               // used to iterate w nodes
    var _index = 0
    val s = Stack[Int]()
    val isRemoved = BitSet()
    val strongconnect = Stack[StackFrame]()

    (0 until qVert).foreach { v_idx =>
      if(index(v_idx) == -1) {
        strongconnect.push(StackFrame(v_idx, SetDepth))
        while(!strongconnect.isEmpty) {
          val StackFrame(v, step) = strongconnect.pop()
          step match {
            case SetDepth =>
              index(v) = _index
              lowlink(v) = _index
              _index += 1
              s.push(v)
              isRemoved.remove(v)
              strongconnect.push(StackFrame(v, ConsiderSuccessors))

            case ConsiderSuccessors =>
              if(wIndex(v) < exit(v).size){
                val w = exit(v)(wIndex(v))
                if(index(w) == -1){
                  strongconnect.push(StackFrame(v, CalcLowlink))
                  strongconnect.push(StackFrame(w, SetDepth))
                }
                else{
                  if(!isRemoved.contains(w)){
                    if(lowlink(v) > lowlink(w)) lowlink(v) = index(w)
                  }
                  wIndex(v) += 1
                  strongconnect.push(StackFrame(v, ConsiderSuccessors))
                }
              }
              else{
                strongconnect.push(StackFrame(v, PopIfRoot))
              }

            case CalcLowlink =>
              val w = exit(v)(wIndex(v))
              if(lowlink(v) > lowlink(w)) lowlink(v) = lowlink(w)
              wIndex(v) += 1
              strongconnect.push(StackFrame(v, ConsiderSuccessors))

            case PopIfRoot =>
              if(index(v) == lowlink(v)){
                val buf = Buffer[A]()
                var w = 0
                do{
                  w = s.pop()
                  isRemoved += w
                  buf += verts(w)
                }
                while(w != v)
                result += buf.toSeq
              }
          }
        }
      }
    }
    result.toSeq
  }

  lazy val hasCycle = tarjan_iterative.find(_.size >= 2).isDefined

  lazy val topologicalSort =
    if(hasCycle) None
    else         Some(tarjan_iterative.flatten.reverse)

}

运行维基百科文章中的示例图:

val g = new SparseDG(Seq(
        Arc("1","2"),
        Arc("2","3"),
        Arc("3","1"),
        Arc("4","2"),
        Arc("4","3"),
        Arc("6","3"),
        Arc("6","7"),
        Arc("7","6"),
        Arc("4","5"),
        Arc("5","4"),
        Arc("5","6"),
        Arc("8","5"),
        Arc("8","8"),
        Arc("8","7")
      ))

g.tarjan_iterative

返回:

ArrayBuffer(ArrayBuffer(1, 3, 2), ArrayBuffer(7, 6), ArrayBuffer(4, 5), ArrayBuffer(8))
于 2015-02-18T15:16:02.447 回答
0

我知道这篇文章很旧,但我最近一直在 Scala 中实现 Tarjans 算法。在代码的实现中,我正在查看这篇文章,我突然想到,它可以以更简单的方式完成:

case class Edge[A](from: A, to: Set[A])

class TarjanGraph[A](src: Iterable[Edge[A]]) {
  lazy val trajan: mutable.Buffer[mutable.Buffer[A]] = {
    var s = mutable.Buffer.empty[A] //Stack to keep track of nodes reachable from current node
    val index = mutable.Map.empty[A, Int] //index of each node
    val lowLink = mutable.Map.empty[A, Int] //The smallest index reachable from the node
    val ret = mutable.Buffer.empty[mutable.Buffer[A]] //Keep track of SCC in graph
def visit(v: A): Unit = {
  //Set index and lowlink of node on first visit
  index(v) = index.size
  lowLink(v) = index(v)
  //Add to stack
  s += v
  if (src.exists(_.from == v)) {
    for (w <- src.find(e => e.from == v).head.to) {
      if (!index.contains(w)) { //Node is not explored yet
        //Perform DFS from node W
        visit(w)
        //Update the lowlink value of v so it has the value of the lowest node reachable from itself and from node w
        lowLink(v) = math.min(lowLink(w), lowLink(v))
      } else if (s.contains(w)) {
        // Node w is on the stack meaning - it means there is a path from w to v
        // and since node w is a neighbor to node v there is also a path from v to w
        lowLink(v) = math.min(lowLink(v), index(w))
      }
    }
  }
  //The lowlink value haven't been updated meaning it is the root of a cycle/SCC
  if (lowLink(v) == index(v)) {
    //Add the elements to the cycle that has been added to the stack and whose lowlink has been updated by node v's lowlink
    //This is the elements on the stack that is placed behind v
    val n = s.length - s.indexOf(v)
    ret += s.takeRight(n)
    //Remove these elements from the stack
    s.dropRightInPlace(n)
  }
}

//Perform a DFS from  all no nodes that hasn't been explored
src.foreach(v => if (!index.contains(v.from)) visit(v.from))
ret
  }

  // A cycle exist if there is a SCC with at least two components
  lazy val hasCycle: Boolean = trajan.exists(_.size >= 2)
  lazy val trajanCycle: Iterable[Seq[A]] = trajan.filter(_.size >= 2).distinct.map(_.toSeq).toSeq
  lazy val topologicalSortedEdges: Seq[Edge[A]] =
    if (hasCycle) Seq[Edge[A]]()
    else trajan.flatten.reverse.flatMap(x => src.find(_.from == x)).toSeq
}
于 2020-02-14T09:23:30.207 回答