Question

我有一个存储在Map数据结构中的有向图，其中键是节点的ID 并且[value]是关键节点指向的节点的nodeIds的数组。

Map<String, String[]> map = new HashMap<String, String[]>();
map.put("1", new String[] {"2", "5"});
map.put("2", new String[] {"3"});
map.put("3", new String[] {"4"});
map.put("4", new String[] {"4"});
map.put("5", new String[] {"5", "9"});
map.put("6", new String[] {"5"});
map.put("7", new String[] {"6"});
map.put("8", new String[] {"6"});
map.put("9", new String[] {"10"});
map.put("10", new String[] {"5"});
map.put("11", new String[] {"11"});

我写了一个递归搜索算法，试图在图中找到圆圈。

Set<String> nodes = map.keySet();

    for(String node : nodes) {
        List<String> forbiddens = new ArrayList<>(); // This list stores the touched nodes, during the process.
        forbiddens.add(node);
        recursiveSearch(node, forbiddens);
    }

该功能由上面的代码调用。

private void recursiveSearch(String nodeId, List<String> forbiddens) {
    String[] neighbours = map.get(nodeId); // The given node's neighbours
    for(String neighbour : neighbours) {
        for(String forbidden : forbiddens) {
            if(neighbour.equals(forbidden)) {
                ways.add( getClone(forbidden) ); //getClone returns the copy of a given List, "ways" is a List<List<String>> which contains the lists of paths which are leading to a circle in the graph
                return;
            }
        }
        forbiddens.add(neighbour);
        recursiveSearch(neighbour, forbiddens);
        forbiddens.remove(neighbour);
    }
}

有些路径包含我想要删除的额外节点（不在圆圈中）。我想请求帮助从“方式”列表中选择节点以获取圆的实际节点。

此算法可以在图表中找到所有圆圈吗？

Answer 1

由于有向图中的圆圈表示强连接组件，因此您可以使用维基百科页面上引用的任何算法来查找强连接组件https://en.wikipedia.org/wiki/Strongly_connected_component - 例如基于Tarjan的算法深度优先搜索：https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm

编辑：强连接组件可能包含多个彼此共享节点的圆圈。因此，必须手动检查每个组件，但应该很容易。

Answer 2

package neo4j

import java.net.URI
import org.apache.spark.graphx.{Edge, EdgeRDD, Graph, Pregel, VertexId, VertexRDD}
import org.apache.spark.rdd.RDD
import org.opencypher.spark.api.CAPSSession
import org.apache.spark.sql.types._
import org.apache.spark.sql.functions._
import org.apache.spark.sql.{DataFrame, Row}
import org.opencypher.okapi.api.graph.GraphName
import org.opencypher.okapi.api.io.conversion.{NodeMapping, RelationshipMapping}
import org.opencypher.spark.api.io.neo4j.{Neo4jConfig, Neo4jPropertyGraphDataSource}
import org.opencypher.spark.api.io.{CAPSNodeTable, CAPSRelationshipTable}
import org.opencypher.spark.impl.io.neo4j.external.Neo4j
import scala.collection.mutable
import scala.collection.mutable.ListBuffer
import scala.util.Random
import scala.util.control.Breaks

object TestV  extends App {
  //1) Create CAPS session and retrieve Spark session
  implicit val session: CAPSSession = CAPSSession.local()
  val spark = session.sparkSession
  //11)  Connect to Neo4j
  val boltWriteURI: URI = new URI("bolt://localhost:7687")
  val neo4jWriteConfig: Neo4jConfig = new Neo4jConfig(boltWriteURI, "neo4j", Some("123abc"), true)
  val neo4jResult: Neo4jPropertyGraphDataSource = new Neo4jPropertyGraphDataSource(neo4jWriteConfig)(session)
  val neo4jConnection = Neo4j(neo4jWriteConfig, session.sparkSession)

  val neo4jResultName: GraphName = new GraphName("neo4jgraph")
  neo4jResult.delete(neo4jResultName)
  //node : no, name;  relation : source, target, amount
  val len = 9
  var node_seq = collection.mutable.ListBuffer[(Long, String)]()
  var relation_seq = collection.mutable.ListBuffer[(Long, Long, Double)]()
  for (i <- 0 until len) {
    node_seq.+=((i.toLong, s"name$i"))
    i match {
      case a if a == len - 1 => relation_seq.+=((0.toLong, a.toLong, Random.nextDouble() * len))
      case _ => relation_seq = relation_seq.+=((i + 1.toLong, i.toLong, Random.nextDouble() * len))
    }
    if (i % 10 == 0) {
      Thread.sleep(100)
      //println(node_seq.length + " " + relation_seq.length)
    }
  }
  //println(node_seq)
  //println(relation_seq)
  node_seq.+=((9.toLong, "name9"))
  node_seq.+=((10.toLong, "name10"))
  node_seq.+=((11.toLong, "name11"))
  node_seq.+=((12.toLong, "name12"))
  relation_seq.+=((0L, 0L, Random.nextDouble() * len))
  relation_seq.+=((3L, 3L, Random.nextDouble() * len))
  relation_seq.+=((0L, 3L, Random.nextDouble() * len))
  relation_seq.+=((0L, 9L, Random.nextDouble() * len))
  relation_seq.+=((7L, 10L, Random.nextDouble() * len))
  relation_seq.+=((10L, 7L, Random.nextDouble() * len))
  relation_seq.+=((7L, 10L, Random.nextDouble() * len))
  relation_seq.+=((10L, 7L, Random.nextDouble() * len))
  relation_seq.+=((10L, 11L, Random.nextDouble() * len))
  relation_seq.+=((11L, 12L, Random.nextDouble() * len))
  relation_seq.+=((12L, 10L, Random.nextDouble() * len))

  relation_seq.+=((0L, 0L, Random.nextDouble() * len))
  relation_seq.+=((3L, 3L, Random.nextDouble() * len))
  relation_seq.+=((3L, 0L, Random.nextDouble() * len))
  relation_seq.+=((9L, 0L, Random.nextDouble() * len))
  relation_seq.+=((10L, 7L, Random.nextDouble() * len))
  relation_seq.+=((7L, 10L, Random.nextDouble() * len))
  relation_seq.+=((10L, 7L, Random.nextDouble() * len))
  relation_seq.+=((7L, 10L, Random.nextDouble() * len))
  relation_seq.+=((11L, 10L, Random.nextDouble() * len))
  relation_seq.+=((12L, 11L, Random.nextDouble() * len))
  relation_seq.+=((10L, 12L, Random.nextDouble() * len))

  //3) cache the dataframe
  //println("#####" +node_seq.length + " " + relation_seq.length)
  val nodesDF: DataFrame = spark.createDataFrame(node_seq).toDF("no", "name").
    withColumn("id1", monotonically_increasing_id()).select("id1", "name", "no").cache()
  nodesDF.count()
  //nodesDF.show
  val relsDF: DataFrame = spark.createDataFrame(relation_seq).toDF("source", "target", "amount").
    withColumn("id2", monotonically_increasing_id()).select("id2", "source", "target", "amount").cache()
  relsDF.count()
  //relsDF.show

  import spark.implicits._

  //8) mapping the columns
  val node_mapping = NodeMapping.withSourceIdKey("id1").withImpliedLabel("Person").withPropertyKeys("no", "name")
  val rel_mapping = RelationshipMapping.withSourceIdKey("id2").withSourceStartNodeKey("source")
    .withSourceEndNodeKey("target").withRelType("KNOWS").withPropertyKeys("amount")

  //9)  create tables
  val node_table = CAPSNodeTable(node_mapping, nodesDF)
  val rel_table = CAPSRelationshipTable(rel_mapping, relsDF)

  //10) Create graph
  val graph = session.readFrom(node_table, rel_table)

  //12) Store graph in neo4j
  neo4jResult.store(neo4jResultName, graph)
  val node_result = neo4jConnection.cypher("MATCH (n:Person) RETURN n.no as no, n.name as name").loadNodeRdds
  val node_fields: Array[StructField] = Array(new StructField("no", LongType, true), StructField("name", StringType, true))
  val nodeSchema = new StructType().add(node_fields(0)).add(node_fields(1))
  //session.sparkSession.createDataFrame(node_result, nodeSchema).show(10)
  val rel_result = neo4jConnection.rels("MATCH (m:Person)-[r:KNOWS]->(n:Person) RETURN m.no as source, n.no as target, r.amount as amount").loadRelRdd
  val rel_fields: Array[StructField] = Array(new StructField("source", LongType, true), StructField("target", LongType, true),
    StructField("amount", DoubleType, true))
  val relSchema = new StructType().add(rel_fields(0)).add(rel_fields(1)).add(rel_fields(2))
  //session.sparkSession.createDataFrame(rel_result, relSchema).show(10)
  val edges: EdgeRDD[Double] = EdgeRDD.fromEdges(rel_result.map { case Row(a: Long, b: Long, c: Double) => Edge(a, b, c) })
  val vertices: VertexRDD[(Long, String)] = VertexRDD(node_result.map { case Row(a: Long, b: String) => (a, (a, b)) })
  val graph_spark = Graph[(Long, String), Double](vertices, edges)
  val final_graph_fit_tmp1 = graph_spark.removeSelfEdges().mapVertices((id, attr) =>
    (new collection.mutable.HashMap[Long, collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]]().+=
    ((id, new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]().+=
    (collection.mutable.LinkedHashSet[Long](id))))
      , new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]](), 0))

  val find_circle = Pregel(final_graph_fit_tmp1, new collection.mutable.HashMap
    [Long, collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]]())(
    (id, attr, msg) => {
      Thread.sleep(10)
      if (id == 4) {
        println("================================")
        println("                " + attr._3 + "                ")
        println("================================")
      }
      println("id: " + id + " msg: " + msg + " attr: " + attr)
      val ss: collection.mutable.HashMap[Long, collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]] =
        new collection.mutable.HashMap[Long, collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]]()
      for (ss_a <- attr._1) {
        val cpy = new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]()
        for (e <- ss_a._2) {
          cpy.+=(e)
        }
        ss.+=(ss_a._1 -> cpy)
        if (msg.contains(ss_a._1)) {
          for (s_m <- msg(ss_a._1)) {
            for (s_a <- ss_a._2) {
              if (attr._3 == 3 && id == 11)
                println("order operate: " + s_a + " " + s_m)
              if (s_a.-(s_a.head) == s_m.-(s_m.last))
                ss(ss_a._1).+=(s_a.++(s_m))
              if (attr._3 > 1) {
                val set = new collection.mutable.HashSet[Int]()
                for (i <- ss(ss_a._1).indices) {
                  if (ss(ss_a._1)(i) == (s_a)) {
                    set.add(i)
                  }
                }
                val set2 = ss(ss_a._1).indices.toSet.diff(set)
                val listBuf = new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]()
                for (i <- set2) {
                  listBuf.append(ss(ss_a._1)(i))
                }
                ss(ss_a._1).clear()
                ss(ss_a._1).append(listBuf:_*)
              }
            }
          }
        }
      }
      for (key <- msg.keys.toSet.diff(ss.keys.toSet)) {
        val cpy = new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]()
        for (e <- msg(key)) {
          cpy.+=(e)
        }
        ss.+=((key, cpy))
      }
      val set_remove: collection.mutable.ListBuffer[(Long, collection.mutable.LinkedHashSet[Long])] =
        new collection.mutable.ListBuffer[(Long, collection.mutable.LinkedHashSet[Long])]()
      for (s <- ss) {
        for (e <- s._2) {
          if (attr._3 > 0) {
            if (e.isEmpty) {
              set_remove.+=((s._1, e))
            } else if (attr._3 == 1) {
              ss.remove(id)
            } else if (e.contains(id) || e.size != attr._3) {
              set_remove.+=((s._1, e))
              if (e.size == attr._3) {
                attr._2.+=(e)
              }
            }
          }
        }
      }
      for (s <- set_remove) {
        val set = new collection.mutable.HashSet[Int]()
        for (i <- ss(s._1).indices) {
          if (ss(s._1)(i) == s._2) {
            set.add(i)
          }
        }
        val set2 = ss(s._1).indices.toSet.diff(set)
        val listBuf = new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]()
        for (i <- set2) {
          listBuf.append(ss(s._1)(i))
        }
        ss(s._1).clear()
        ss(s._1).append(listBuf:_*)
      }
      (ss.filter(s => s._2.nonEmpty), attr._2.filter(s => s.nonEmpty), attr._3 + 1)
    },
    trp => if (trp.srcAttr._1.keys.nonEmpty) {
      val ss = new collection.mutable.HashMap[Long, collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]]()
      for (s <- trp.srcAttr._1) {
        if (ss.contains(trp.srcId)) {
          ss(trp.srcId).++=(s._2)
        } else {
          val cpy = new collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]()
          for (e <- s._2 if e.size - trp.srcAttr._3 < 2 && e.size - trp.srcAttr._3 > -2 && e.size - trp.dstAttr._3 < 2 && e.size - trp.dstAttr._3 > -2) {
            cpy.+=(e)
          }
          if (cpy.nonEmpty)
            ss.+=(trp.srcId -> cpy)
        }
      }
      if (ss.nonEmpty)
        Iterator({
          (trp.dstId, ss)
        })
      else
        Iterator.empty
    } else Iterator.empty,
    (a, b) => {
      val ss = new collection.mutable.HashMap[Long, collection.mutable.ListBuffer[collection.mutable.LinkedHashSet[Long]]]()
      ss.++=(a)
      ss.++=(b)
      ss
    }).cache()
  println("================================")
  println("                vertices                ")
  println("================================")
  p**rintln(find_circle.vertices.mapValues(v => v._2.toSet).take(15).mkString("##;\r\n"))
  System.exit(0)
}

输出：

================================
                0                
================================
id: 4 msg: Map() attr: (Map(4 -> ListBuffer(Set(4))),ListBuffer(),0)
id: 11 msg: Map() attr: (Map(11 -> ListBuffer(Set(11))),ListBuffer(),0)
id: 0 msg: Map() attr: (Map(0 -> ListBuffer(Set(0))),ListBuffer(),0)
id: 1 msg: Map() attr: (Map(1 -> ListBuffer(Set(1))),ListBuffer(),0)
id: 6 msg: Map() attr: (Map(6 -> ListBuffer(Set(6))),ListBuffer(),0)
id: 3 msg: Map() attr: (Map(3 -> ListBuffer(Set(3))),ListBuffer(),0)
id: 12 msg: Map() attr: (Map(12 -> ListBuffer(Set(12))),ListBuffer(),0)
id: 9 msg: Map() attr: (Map(9 -> ListBuffer(Set(9))),ListBuffer(),0)
id: 7 msg: Map() attr: (Map(7 -> ListBuffer(Set(7))),ListBuffer(),0)
id: 8 msg: Map() attr: (Map(8 -> ListBuffer(Set(8))),ListBuffer(),0)
id: 10 msg: Map() attr: (Map(10 -> ListBuffer(Set(10))),ListBuffer(),0)
id: 5 msg: Map() attr: (Map(5 -> ListBuffer(Set(5))),ListBuffer(),0)
id: 2 msg: Map() attr: (Map(2 -> ListBuffer(Set(2))),ListBuffer(),0)
================================
                1                
================================
id: 4 msg: Map(5 -> ListBuffer(Set(5))) attr: (Map(4 -> ListBuffer(Set(4))),ListBuffer(),1)
id: 11 msg: Map(10 -> ListBuffer(Set(10)), 12 -> ListBuffer(Set(12))) attr: (Map(11 -> ListBuffer(Set(11))),ListBuffer(),1)
id: 0 msg: Map(1 -> ListBuffer(Set(1)), 3 -> ListBuffer(Set(3)), 9 -> ListBuffer(Set(9))) attr: (Map(0 -> ListBuffer(Set(0))),ListBuffer(),1)
id: 1 msg: Map(2 -> ListBuffer(Set(2))) attr: (Map(1 -> ListBuffer(Set(1))),ListBuffer(),1)
id: 6 msg: Map(7 -> ListBuffer(Set(7))) attr: (Map(6 -> ListBuffer(Set(6))),ListBuffer(),1)
id: 3 msg: Map(4 -> ListBuffer(Set(4)), 0 -> ListBuffer(Set(0))) attr: (Map(3 -> ListBuffer(Set(3))),ListBuffer(),1)
id: 12 msg: Map(11 -> ListBuffer(Set(11)), 10 -> ListBuffer(Set(10))) attr: (Map(12 -> ListBuffer(Set(12))),ListBuffer(),1)
id: 9 msg: Map(0 -> ListBuffer(Set(0))) attr: (Map(9 -> ListBuffer(Set(9))),ListBuffer(),1)
id: 7 msg: Map(8 -> ListBuffer(Set(8)), 10 -> ListBuffer(Set(10))) attr: (Map(7 -> ListBuffer(Set(7))),ListBuffer(),1)
id: 8 msg: Map(0 -> ListBuffer(Set(0))) attr: (Map(8 -> ListBuffer(Set(8))),ListBuffer(),1)
id: 10 msg: Map(11 -> ListBuffer(Set(11)), 7 -> ListBuffer(Set(7)), 12 -> ListBuffer(Set(12))) attr: (Map(10 -> ListBuffer(Set(10))),ListBuffer(),1)
id: 5 msg: Map(6 -> ListBuffer(Set(6))) attr: (Map(5 -> ListBuffer(Set(5))),ListBuffer(),1)
id: 2 msg: Map(3 -> ListBuffer(Set(3))) attr: (Map(2 -> ListBuffer(Set(2))),ListBuffer(),1)
....
....
================================
                    9                
================================
....
....
================================
                vertices                
================================
(4,Set(Set(5, 6, 7, 8, 0, 3, 4), Set(5, 6, 7, 8, 0, 1, 2, 3, 4)))##;
(11,Set(Set(10, 11), Set(12, 11), Set(10, 12, 11)))##;
(0,Set(Set(1, 2, 3, 4, 5, 6, 7, 8, 0), Set(3, 4, 5, 6, 7, 8, 0), Set(9, 0), Set(1, 2, 3, 0), Set(3, 0)))##;
(1,Set(Set(2, 3, 0, 1), Set(2, 3, 4, 5, 6, 7, 8, 0, 1)))##;
(6,Set(Set(7, 8, 0, 3, 4, 5, 6), Set(7, 8, 0, 1, 2, 3, 4, 5, 6)))##;
(3,Set(Set(0, 3), Set(0, 1, 2, 3), Set(4, 5, 6, 7, 8, 0, 3), Set(4, 5, 6, 7, 8, 0, 1, 2, 3)))##;
(12,Set(Set(11, 12), Set(10, 12), Set(11, 10, 12)))##;
(9,Set(Set(0, 9)))##;
(7,Set(Set(10, 7), Set(8, 0, 3, 4, 5, 6, 7), Set(8, 0, 1, 2, 3, 4, 5, 6, 7)))##;
(8,Set(Set(0, 3, 4, 5, 6, 7, 8), Set(0, 1, 2, 3, 4, 5, 6, 7, 8)))##;
(10,Set(Set(11, 10), Set(7, 10), Set(12, 10), Set(11, 12, 10)))##;
(5,Set(Set(6, 7, 8, 0, 3, 4, 5), Set(6, 7, 8, 0, 1, 2, 3, 4, 5)))##;
(2,Set(Set(3, 0, 1, 2), Set(3, 4, 5, 6, 7, 8, 0, 1, 2)))

Process finished with exit code 0

检测图表中的所有圆圈

2 个答案: